DESCRIPTIVE  ASTRONOMY 


AN  ELEMENTARY  EXPOSITION  OF  THE  FACTS,  PRINCIPLES, 
AND  THEORIES  OF  ASTRONOMICAL  SCIENCE 


By 

FOREST  RAY  MOULTON,  A.B.,  PH.D. 

PROFESSOR  OF  ASTRONOMY,  THE  UNIVERSITY  OF   CHICAGO;    RESEARCH 
ASSOCIATE,  CARNEGIE  INSTITUTION  OF  WASHINGTON)  MEMBER, 

NATIONAL  ACADEMY   OF   SCIENCES;  FELLOW,  ROYAL 

ASTRONOMICAL  SOCIETY;  AUTHOR  OF  "CELESTIAL 

MECHANICS,"  "PERIODIC  ORBITS" 


ILLUSTRATED 


CHICAGO 

AMERICAN  SCHOOL  OF  CORRESPONDENCE 
1912 


COPYRIGHT  1912  B? 
AMERICAN  SCHOOL  OP  CORRESPONDENCE 


Entered  at  Stationers'  Hall,  London 
All  Rights  Reserved 


CONTENTS 


PRELIMINARY  CONSIDERATIONS 

Page 

Value  of  science 1 

Origin  of  science 2 

Great  contributions  of  astronomy  to  science 3 

Present  value  of  astronomy 4 

Scope  of  astronomy 6 

THE  EARTH  AS  AN  ASTRONOMICAL  BODY 

Astronomical  problems  respecting  the  earth 7 

Proofs  that  the  earth  is  round 8 

•Oblateness  of  the  earth 10 

Size  of  the  earth 13 

-Different  kinds  of  latitude 13 

•Density  of  the  earth 14 

Condition  of  interior  of  the  earth 15 

Composition  of  the  earth's  atmosphere 18 

Height  of  the  earth's  atmosphere 18 

Kinetic  theory  of  gases 21 

Escape  of  atmospheres 23 

Effects  of  atmosphere  on  climate 25 

Refraction  of  light  by  the  atmosphere 28 

Relative  rotation  of  the  earth 30 

Laws  of  motion , 32 

Rotation  of  the  earth  proved  by  eastward  deviation  of  falling  bodies.  ...  34 

Rotation  of  the  earth  proved  by  its  shape 35 

•Rotation  of  the  earth  proved  by  Foucault's  pendulum  experiment 36 

Analogy  with  other  heavenly  bodies 37 

Uniformity  of  the  earth's  rotation 38 

•Variation  of  latitude 40 

Apparent  motion  of  the  sun  with  respect  to  the  stars 42 

•Revolution  of  the  earth  proved  by  the  parallax  of  the  stars 44 

'Revolution  of  the  earth  proved  by  aberration  of  light 46 

'  Revolution  of  the  earth  proved  by  the  spectroscope 47 

Shape  of  the  earth's  orbit 48 

Obliquity  of  the  ecliptic 49 

•Precession  of  the  equinoxes 50 

Causes  of  the  seasons 51 

Relative  amounts  of  sunlight  in  different  latitudes 54 

Lag  of  the  seasons 57 

Effect  of  the  eccentricity  of  the  earth's  orbit  upon  the  seasons 58 


CONTENTS 

Page 
THE   CONSTELLATIONS 

Problem  of  locating  the  constellations 61 

Geographical  system 62 

Horizon  system 63 

Equator  system 64 

Ecliptic  system 67 

Comparison  of  systems 68 

Determination  of  right  ascension  of  meridian  at  any  time 69 

Application  of  declination  to  location  of  stars 71 

Origin  of  constellations 72 

Naming  the  stars 79 

Star  catalogues 80 

Magnitudes  of  stars 82 

First-magnitude  stars 85 

Number  of  stars 85 

fet  Proper  motions  of  stars. . .  .• 87 

Milky  Way  or  Galaxy 88 

How  to  find  the  pole  star 90 

Cassiopeia. 92 

Equinoxes 93 

Lyra ". 93 

Scorpio 95 

Bootes 95 

Leo 96 

Taurus 96 

Orion 97 

Canis  major 100 . 

Gemini. 100 

TIME 

Definition  of  equal  intervals  of  time 100 

-Sidereal  time 101 

-Solar  time 102 

-•Mean  solar  time 103 

.-Standard  time 105 

Civil  and  astronomical  days 107 

Place  of  change  of  date 107 

-  Sidereal  year 108 

-Tropical  year 108 

Calendar 109 

THE  MOON 

—  Moon's  apparent  motion  among  the  stars 110 

Moon's  phases Ill 

Distribution  of  sunlight  and  moonlight 113 

Distance  of  the  moon 113 

Moon's  actual  motion. . 117 


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CONTENTS 

Page 

Size  of  the  moon 118 

Mass  of  the  moon 119 

Atmosphere  of  the  moon 120 

Light  and  heat  received  by  the  earth  from  the  moon 121 

Temperature  of  the  moon 122 

Surface  conditions  on  the  moon 123 

Eclipses  of  the  moon 131 

Eclipses  of  the  sun 132 

Relative  number  of  eclipses  of  sun  and  moon  as  observed  from  any  one 

place 133 


THE   SOLAR   SYSTEM 

Members  of  the  solar  system 137 

Orbits  of  the  planets .  138 

Law  of  gravitation 139 

Distances  of  the  planets -. 141 

Dimensions  and  masses  of  planets 144 

Periods  of  the  planets 147 

Two  groups  of  planets 151 

Planetoids 152 

Zodiacal  light  and  gegenschein 157 

Mercury  and  Venus 159 

Mars 161 

Jupiter 170 

Saturn ... 175 

Uranus 179 

Neptune , 181 


COMETS   AND   METEORS 

Orbits  of  comets 185 

Dimensions  and  masses  of  comets 186 

Capture  of  comets 187 

Celebrated  comets 190 

Meteors  or  shooting  stars  192 

Relation  of  comets  and  meteors 194 

Influences  of  meteors  on  the  earth 195 

Meteorites..                                                                                                          ,  196 


THE   SUN 

Light  and  heat  received  from  the  sun 197 

Source  of  the  sun's  heat 200 

Sun  spots 204 

Different  layers  of  the  sun 206 

Spectrum  analysis 210 


CONTENTS 

Page 
THE   SIDEREAL   SYSTEM 

Distribution  of  stars 216 

Groups  of  stars 219 

Double  stars 224 

Spectroscopic  binary  stars 227 

Variable  stars 229 

Temporary  stars 231 

Nebulas 233 

COSMOGONY  OR  THE  EVOLUTION   OF  WORLDS 

Evolution 235 

Historical 237 

Test  of  the  Laplacian  theory 241 

Planetesimal  theory 244 

Conclusion. .                            250 


HALLEY'S    COMET 

This  picture  was  taken  at  Yerkes  Observatory  on  May  4,  1910,  with  an  exposure  of  forty  minutes. 

The  tail  is  about  8°  long 


INTRODUCTION 


ASTRONOMY  has  the  glory  of  being  the  oldest  science.  In 
fact,  men  first  realized  from  the  majestic  and  relatively  sim- 
ple motions  of  the  heavenly  bodies  that  the  universe  is  a  universe 
of  order  and,  therefore,  that  science  is  possible.  If  the  sky  had  been 
always  cloudy,  if  observations  could  not  have  extended  beyond  the 
exceedingly  complex  and  varying  terrestrial  phenomena,  it  is  prob- 
able that  many  centuries  would  have  passed  before  scientists  would 
have  arrived  at  the  point  of  view  which  was  necessary  for  the  devel- 
opment of  those  ideas  which  have  led  to  the  wonderful  discoveries 
of  modern  times.  It  is  appropriate,  therefore,  that  a  book  on  Astron- 
omy should,  among  other  things,  show  the  connection  of  celestial 
phenomena  with  the  important  intellectual  achievements  of  civilized 
man,  a  phase  of  the  subject  which  has  not  been  neglected  in  this 
work. 

C.  There  are  two  chief  features  to  science — the  making  of  observa- 
tions, and  the  fitting  of  them  into  an  organized  whole.  In  this  text 
detailed  instructions  have  been  given  so  that  the  reader  may  make 
such  of  these  observations  as  do  not  require  the  use  of  instruments, 
but  it  is  evident  that  such  observations  can  not  add  much  to  the 
world's  knowledge  at  the  present  time.  However,  their  performance 
demands  the  active  instead  of  the  passive  attitude  of  the  mind ;  they 


give  something  of  the  satisfaction  that  is  experienced  by  an  original 
discoverer;  and  they  make  every  glance  at  the  familiar  stars  which 
fill  the  sky  on  a  cloudless  night  one  of  pleasure.  Great  care  has 
been  taken  also  to  show  how  the  vast  multitude  of  things,  which 
observations  have  revealed,  are  linked  together  into  a  systematic 
body  of  doctrine,  and  entitle  Astronomy  to  be  regarded  as  one  of 
the  most  perfect  sciences. 

<£  Doubtless  every  person  has  some  more  or  less  definite  conception 
of  what  the  universe  is  and  means,  and  of  his  place  in  it.  All  the 
things  he  knows  and  experiences  modify  this  conception.  The  facts 
revealed  in  Astronomy — the  extent,  variety,  and  lawfulness  of  the 
physical  universe;  that  man  has  in  his  body  the  elements  of  which 
the  infinitely  distant  stars  are  composed;  that  he  is  but  a  part  of 
the  universal  order — effect  profoundly  his  philosophy;  and  this  has 
been  borne  in  mind  in  setting  forth  modern  ideas  of  how  tenuous 
nebulas  evolve  into  finished  worlds 


L 


THE    GREAT    YERKES    40-INCH    TELESCOPE 

The  dome  is  revolved  by  machinery  and  the  entire  floor  is  raised  or  lowered  to  suit  the  inclination  of 

the  telescope  tube 


ASTRONOMY 

PART  I 


PRELIMINARY  CONSIDERATIONS 

The  Value  of  Science.  In  an  age  when  the  world  is  so  largely 
run  by  the  results  of  scientific  effort  it  is  almost  superfluous  to 
speak  of  the  value  of  science.  If  the  things  which  science  has  con- 
tributed to  our  everyday  use  and  which  make  life  at  the  present 
time  pleasant  for  us  were  removed,  we  should  speedily  understand 
the  immense  debt  we  owe  to  it.  One  has  to  think  only  of  the  means 
of  transportation,  communication,  and  illumination  to  see  how  very 
important  it  is  for  us.  These  things  are  so  well  known  that  they 
do  not  need  emphasis. 

There  is  an  indirect  result  in  the  work  of  scientists  which  is  not 
so  generally  understood,  and  to  which  we  seldom  give  any  considera- 
tion. Science  has  revolutionized  our  mode  of  living,  that  is,  it  has 
given  us  a  better  food  supply  than  any  people  ever  had ;  because  of 
it,  we  are  better  sheltered  and  clothed  than  any  people  ever  have 
been ;  our  whole  mode  of  living  is  more  sanitary  than  that  of  any 
other  people  has  been;  and  these  facts  will  eventually  result  in 
marked  physical  changes  in  mankind  as  the  generations  go  by.  Thus, 
while  we  are  apt  to  consider  that  science  pertains  largely  to  the 
inanimate  part  of  the  universe,  we  see  that  it  is  not  only  of  the  highest 
value  indirectly  to  the  organic  portion,  but  to  man  as  well.  If  we 
are  considering  things  in  the  long  run,  this  latter  may  be  the  one 
respect  in  which  it  is  most  valuable. 

It  is  a  common  opinion  that  science  is  distinguished  from  the 
fine  arts  and,  in  fact,  is  opposed  to  them.  Science  and  the  fine  arts 
are  very  often  supposed  to  be  the  antithesis  of  each  other.  But  one 
of  the  results  of  science  has  been  that  it  has  made  us  immensely 
more  efficient  than  we  were  before,  and  through  its  teachings  we  are 
enabled  to  provide  the  necessities  and  even  the  luxuries  of  life  in 
much  less  time  than  was  possible  before  its  modern  development. 

Copyright,  1912,  by  American  School^pf  Correspondence. 


2  ASTRONOMY 

The  leisure  which  has  been  secured  thereby  will  enable  us  to  turn 
our  attention  to  the  arts  and  undoubtedly  in  the  future  to  achieve 
greater  things  in  this  direction  than  would  otherwise  have  been 
possible. 

It  is  a  mistake  to  regard  science  in  itself  as  the  opposite  of  art. 
There  are  in  all  branches  of  science  harmonies  and  beauties  which 
appeal  strongly  to  those  who  fully  understand  them.  The  great 
scientists  have  often  expressed  themselves  as  deeply  moved  by  the 
esthetic  side  of  their  subject. 

Science  also  plays  an  important  role  in  the  mental  discipline. 
If  it  is  a  good  thing  to  think  coherently  and  systematically  and  to 
check  the  results  of  thinking,  then  science  is  of  the  highest  value  in 
the  cultivation  of  the  intellect. 

Origin  of  Science.  It  is  doubtful  if  any  important  idea  ever 
sprang  suddenly  into  the  mind  of  a  single  man.  The  great  move- 
ments in  the  world  have  had  long  epochs  of  preparation,  and  there 
are  evidences  that  many  men  were  groping  for  the  same  idea  without 
exactly  seizing  it. 

The  actual  dawn  of  science  was  in  prehistoric  times,  in  the 
civilizations  that  flourished  in  the  valleys  of  the  Nile  and  the 
Euphrates.  In  the  very  earliest  records  that  have  come  down  to  us 
it  has  been  found  that  those  peoples  knew  much  of  astronomical 
phenomena  and  had  coherent  ideas  of  the  apparent  motions  of  the 
sun,  moon,  planets,  and  stars.  It  is  perfectly  clear  from  their 
writings  that  it  was  first  in  observing  celestial  phenomena  that 
they  obtained  the  idea  that  the  universe  was  not  a  chaos.  Day  and 
night  were  seen  to  succeed  each  other  regularly,  the  moon  passed 
through  its  phases  systematically,  the  seasons  followed  one  another 
in  regular  sequence;  and  in  fact  all  the  more  conspicuous  celestial 
phenomena  were  seen  to  recur  in  an  orderly  fashion.  The  dawn  of 
science  may  be  said  to  have  begun  when  men  first  clearly  perceived 
that  there  was  order  in  the  universe  and  that  by  observations  they 
could  discover  what  it  was.  It  is  to  the  glory  of  astronomy  that  its 
phenomena  were  of  such  a  character  that  men  first  perceived  in  this 
realm  that  we  live  in  an  orderly  universe. 

The  ancient  Greeks,  at  a  period  four  or  five  hundred  years  pre- 
ceding the  Christian  Era,  definitely  undertook  to  find  from  systematic 
observations  how  celestial  phenomena  follow  one  another.  Before 


ASTRONOMY  3 

their  time,  observations  were,  indeed,  made  extending  over  long 
intervals,  but  without  a  conscious  effort  to  attain  the  laws  according 
to  which  the  universe  moves.  The  Greeks  determined  very  accu- 
rately the  number  of  days  in  a  year,  the  number  of  days  in  a  month, 
the  path  of  the  moon  among  the  stars;  they  explained  the  cause  of 
eclipses  and  learned  how  to  predict  them  with  a  considerable  degree 
of  accuracy;  they  undertook  to  determine  the  distances  of  the 
heavenly  bodies,  and  to  work  out  a  complete  system  that  would 
represent  their  motions  for  indefinite  time.  The  idea  was  current 
among  the  Greek  philosophers  that  the  earth  was  round,  that  it 
turned  on  its  axis,  and  among  some  that  it  revolved  around  the  sun. 
Their  science,  in  the  modern  acceptance  of  the  term,  was  largely 
confined  to  the  study  of  celestial  phenomena. 

Great  Contributions  of  Astronomy  to  Science.  As  has  been 
stated,  science  started  in  astronomy.  The  phenomena  of  every  other 
science  are  so  complex  and  depend  upon  so  many  varying  factors 
that  it  would  be  very  difficult  for  a  primitive  people  to  get  the  idea, 
first,  that  there  were  any  laws  operating  in  it,  and  second,  that  they 
could  discover  those  laws.  One  has  to  think  only  of  the  complexities 
in  the  changes  of  the  weather  or  in  the  developments  of  plant  or 
animal  life,  to  see  how  hopeless  a  problem  a  primitive  people  would 
face.  It  is  probably  not  extravagant  to  state  that  if  men  had  not 
been  able  to  observe  celestial  phenomena — for  example,  if  the  sky 
had  always  been  cloudy — the  dawn  of  science  would  have  been 
greatly  delayed.  It  is  entirely  possible  that  we  should  yet  be  in  the 
most  primitive  stages  of  the  development  of  the  race. 

But  we  may  turn  our  attention  to  more  specific  and  direct  con- 
tributions of  astronomy.  Every  one  will  admit  that  mathematics 
has  been  of  the  highest  service  in*  all  domains  of  physical  science. 
It  is  not  so  generally  known  that  the  science  of  mathematics  was 
largely  called  into  being  for  uses  in  explaining  astronomical  phenom- 
ena. Spherical  trigonometry  was  invented  in  very  ancient  times  for 
use  in  solving  the  problems  arising  from  the  celestial  sphere.  And 
this  is  only  one  of  the  many  examples  in  which  some  of  the  most 
important  mathematical  processes  have  been  directly  developed 
as  a  consequence  of  the  stimulus  of  a  problem  set  to  men  in 
astronomy.  While  it  would  undoubtedly  be  too  much  to  claim 
that  all  branches  of  mathematics  have  had  their  original  stimulus  in 


4  ASTRONOMY 

astronomical  problems,  it  is  certain  that  without  these  problems  the 
development  of  mathematics  would  have  been  far  different. 

The  laws  of  motion  are  at  the  very  foundation  of  modern 
mechanics,  and  were  discovered  by  astronomers  contemplating 
astronomical  phenomena.  The  conditions  on  the  earth  are  so 
complex  that  it  would  be  very  difficult  to  comprehend  the  funda- 
mental laws  which  govern  the  movement  of  bodies.  On  the  contrary, 
the  planets  move  in  a  vacuum  without  any  friction,  and  the  con- 
ditions are  so  nearly  ideal  that  discovery  of  these  fundamental 
laws  is  relatively  simple.  It  is  not  too  much  to  say  that  our  knowl- 
edge of  the  laws  of  motion  is  a  contribution  from  astronomy. 

One  of  the  most  important  influences  in  modern  scientific  thought 
is  the  doctrine  of  evolution.  Its  applications  are  not  only  in  geology 
and  zoology,  but  they  are  also  in  the  interpretation  of  history, 
sociology,  and  even  religion.  It  was  in  contemplating  the  relatively 
simple  celestial  phenomena  that  the  idea  of  the  orderly  development 
from  one  state  to  another  was  first  clearly  perceived,  and  the  doctrine 
of  evolution  was  current  in  astronomical  literature  more  than  half  a 
century  before  it  appeared  in  the  writings  of  Darwin  and  his  con- 
temporaries. 

The  modern  world  owes  much  to  the  explorations  that  followed 
the  voyage  of  Columbus  across  the  sea.  It  took  courage  of  the  highest 
type  to  sail  for  many  weeks  over  an  unknown  sea  in  the  frail  boats 
of  that  time.  It  is  perfectly  clear  that  Columbus  had  good  reasons 
for  hoping  that  he  could  reach  the  East  Indies  by  sailing  westward 
from  Europe,  for  otherwise  he  would  not  have  maintained  control  of 
his  mutinous  sailors  for  so  long  a  time.  His  reasons  were  of  an 
astronomical  nature.  He  had  seen  the  sun  rise  from  the  ocean  in 
the  east  and  travel  across  the  s*ky  and  set  in  the  west.  He  had 
observed  that  the  moon  and  stars  did  the  same  thing.  He  concluded 
from  the  fact  that  they  went  down  in  the  west  after  having  pursued 
regular  courses,  and  rose  again  in  the  east  in  the  same  courses,  that 
the  earth  was  not  of  infinite  extent  but  that  it  was  round  and 
could  be  sailed  around.  Relying  upon  the  teachings  of  his  observa- 
tions of  the  motions  of  the  heavenly  bodies,  he  made  the  perilous 
trip  across  the  Atlantic,  and  that  voyage  has  been  of  immense 
importance  to  the  human  race. 

Present  Value  of  Astronomy.     It  is  easy  to  see,  as  has  been 


ASTRONOMY  5 

explained  above,  that  astronomy  has  made  some  great  contributions 
to  the  development  of  science  and  civilization;  but  it  is  commonly 
believed  that  at  the  present  time  it  is  of  little  practical  value  to 
mankind.  This  is  known  as  a  material  age  and  we  are  apt  to  con- 
sider things  valuable  only  if  they  are  valuable  in  a  material  way. 
But  if  astronomy  is  considered  from  this  point  of  view,  we  still  find 
that  it  is  very  important  to  us.  For  example,  navigation  of  the  seas 
is  absolutely  dependent  upon  astronomical  observations.  For  more 
than  two  centuries  France  and  England  gave  prizes  for  accurate 
j  astronomical  tables  that  their  sailors  could  use  in  their  journeys 
(over  the  oceans.  And  at  the  present  time  the  positions  of  vessels 
are  determined  in  all  long  voyages  by  astronomical  observations.  If 
one  were  to  make  a  voyage  to  the  polar  regions  he  would  determine 
This  position,  and  in  particular  whether  he  had  arrived  at  the  earth's 
ipole  or  not,  by  astronomical  observations.  Consequently,  we  may 
say  that  all  the  varied  and  important  interests  which  center  in 
navigation  are  dependent,  even  at  the  present  time,  upon  astronomy. 
One  might  imagine  that,  even  though  astronomy  is  important  to 
sailors,  it  has  little  value  upon  the  land.  Here,  again,  the  first 
impression  is  quite  erroneous.  Every  one  recognizes  how  important 
it  is  that  our  trains  be  run  according  to  accurate  time  schedules. 
It  is  not  so  generally  known,  however,  that  the  time  used  is  based 
upon  astronomical  observations  made  daily.  In  the  National  Observa- 
tory at  Washington  observations  are  made  and  time  is  determined 
and  distributed  every  day  over  the  whole  country.  More  than  30,000 
clocks  are  automatically  set  every  twenty-four  hours  by  the  electric 
signals  which  are  sent  out  from  Washington. 

One  might  ask  whether  some  other  method  of  accurately  meas- 
uring time  might  not  be  devised.  The  general  impression  is  that  a 
clock  might  be  made  to  run  so  accurately  that  it  would  serve  all 
purposes.  The  fact  is,  no  clock  was  ever  made  which  permanently 
ran  accurately.  No  two  can  be  made  to  run  exactly  alike.  In  order 
to  obtain  a  satisfactory  measure  of  time,  the  ideal  conditions  under 
which  the  heavenly  bodies  move  must  be  realized.  Consequently,  a 
second  practical  and  universal  use  of  astronomy  is  in  furnishing  time 
for  mankind. 

There  are  indirect  ways  in  which  astronomy  is  at  the  present  time 
of  great  value.  For  example,  if  it  be  conceded  that  geology  is  an 


6  ASTRONOMY 

important  science,  then  astronomy  must  be  considered  valuable 
because  it  furnishes  the  foundation  for  the  geologist  in  telling  him 
of  the  early  state  of  the  earth.  If  it  is  important  for  man  to  know 
the  laws  of  change  of  the  weather,  then  astronomy  is  again  important 
because  the  reasons  for  the  changing  of  the  weather  are  almost 
entirely  astronomical.  In  this  example  we  have  not  yet  learned 
fully  the  laws  because  they  depend  partly  upon  complex  conditions 
that  are  present  here  upon  the  earth.  The  simple  succession  of 
changes  that  would  follow  from  astronomical  causes  alone  on  a 
uniform  earth  are  modified  by  great  oceans,  continental  elevations, 
and  chains  of  mountains.  Notwithstanding  the  complexity  of  these 
factors,  there  is  hope  of  eventually  reducing  this  domain  of  science 
to  perfect  order. 

While  this  is  called  a  material  age  it  is  probably  not  more  so 
than  most  which  have  preceded  it.  And  if  it  is  not  purely  a  material 
age,  in  estimating  the  value  of  any  science  it  is  proper  to  consider 
its  importance  aside  from  its  practical  applications  to  the  material 
world.  When  considered  from  this  point  of  view  astronomy  is 
probably  second  to  no  other  science.  It  furnishes  man  an  idea 
of  his  place  in  the  universe  and  has  a  profound  influence  upon 
him  in  broadening  his  horizon.  It  is  analogous  to  the  benefits  a 
man  derives  by  traveling  on  the  earth.  If  he  visits  various  countries 
he  learns  many  things  which  he  does  not  directly  apply  at  his  home, 
but  which,  nevertheless,  make  him  a  broader  man.  And  so,  while 
what  one  may  learn  about  worlds  beyond  our  own  can  not,  on  the 
whole,  be  applied  here,  the  broadening  influence  of  the  wider  knowl- 
edge is  very  beneficial.  In  this  way  astronomy  has  had  and  is  having 
profound  influence  on  philosophy  and  literature  and  even  religion. 

Scope  of  Astronomy.  In  astronomy  the  earth  is  considered  first 
as  a  member  of  the  solar  system.  It  is  thought  of  as  a  member  of 
a  family  of  planets  revolving  around  the  sun.  Its  characteristics  as 
one  of  the  heavenly  bodies  are  investigated.  They  are,  in  particular, 
its  shape,  its  size,  its  motions,  its  density,  and  its  interior  condition. 
Then  the  details  of  its  relations  to  other  members  of  the  system  are 
developed  and  the  corresponding  facts  for  the  other  planets  and  the 
sun  are  worked  out. 

There  are  many  secondary  members  of  the  planetary  system, 
among  which  may  be  mentioned  the  satellites  which  revolve  around 


ASTRONOMY  7 

the  planets,  the  comets  which  revolve  around  the  sun,  and  a  great 
number  of  small  planets  which  circulate  mostly  in  the  space  between 
Mars  and  Jupiter.  The  motions  of  these  bodies  and  their  proper- 
ties, and  their  relations  to  the  rest  of  the  system  are  worked  out.  The 
thousands  and  even  millions  of  stars  that  fill  the  sky  are  found  to  be 
suns,  and  the  position  and  relation  of  the  solar  system  with  respect 
to  the  almost  countless  other  systems,  particularly  the  distribution 
of  stars  in  space,  their  motions  and  dimensions,  are  discovered  so 
far  as  it  is  possible.  There  are  also  found  to  be  immense  cloud- 
like  masses  of  unorganized  world-stuff  which  we  call  nebulae,  whose 
number,  positions,  and  relations  to  the  stars  are  discovered. 

In  addition  to  finding  out  what  the  universe  is  at  the  present 
time,  one  of  the  most  important  and  interesting  objects  of  astronomy 
is  to  find  out  how  it  originated,  through  what  series  of  steps  it  has 
gone  in  its  evolution,  and  what  changes  will  take  place  in  it  in  the 
future.  In  particular,  the  astronomer  tries  to  find  out  what  has 
been  the  origin  of  the  earth,  how  long  it  has  been  in  existence,  espe- 
cially in  a  state  adapted  to  the  abode  of  life,  and  what  reasonably 
may  be  expected  for  the  future.  These  great  problems  of  cosmog- 
ony have  been  of  interest  to  mankind  from  the  dawn  of  civilization, 
and  with  increasing  knowledge  they  do  not  lose  their  charm. 

THE   EARTH   AS  AN  ASTRONOMICAL   BODY 

Astronomical  Problems  Respecting  the  Earth.  The  earth  is 
one  of  the  objects  belonging  to  the  field  of  astronomical  investiga- 
tions. It  is  in  considering  it  that  astronomy  has  its  closest  contact 
with  some  of  the  other  sciences,  particularly  with  geology  and  meteor- 
ology. Those  problems  which  can  be  solved  for  the  other  planets 
also,  or  which  are  essential  in  the  investigations  of  other  astronomical 
questions,  are  properly  considered  as  belonging  to  the  field  of  astron- 
omy. 

The  astronomical  problems  pertaining  to  the  earth  are  divided 
into  two  general  classes.  First,  there  are  those  questions  which 
can  be  answered,  at  least  to  a  great  extent,  without  considering  the 
earth  as  a  member  of  the  solar  system.  Second,  there  are  those 
problems  which  pertain  to  it  as  a  member  of  the  solar  family.  Those 
of  the  first  class  are  particularly  its  shape,  size,  density,  rigidity,  and 


8  ASTRONOMY 

its  atmosphere;  while  those  of  the  second  class  are  particularly  its 
motions,  the  heat  and  light  received  from  the  sun,  and  its  evolution. 
We  shall  take  up  first  the  questions  of  the  first  class. 

Proofs  That  the  Earth  Is  Round.  It  is  a  matter  of  common 
knowledge  that  the  earth  is  approximately  round,  but  few  can  give 
the  reasons  for  believing  it.  One  of  the  characteristics  of  science 
is  that  it  gives  the  reasons  for  its  conclusions,  and  consequently  we 
shall  consider  the  methods  by  means  of  which  we  have  proved  the 
sphericity  of  the  earth. 

The  most  commonly  stated  reasons  are  that  the  earth  has  been 
circumnavigated  and  that  the  surface  is  apparently  convex.  While 
this  proves  that  the  earth  is  not  an  infinite  plane,  as  the  ancients 
believed  it  was,  it  does  not  prove  it  is  actually  round;  for  these  con- 
ditions could  be  satisfied  if  its  surface  were  any  closed,  convex  figure, 
even  departing  very  widely  from  a  spherical  form.  There  are  bet- 
ter reasons  for  believing  that  the  earth  is  actually  very  nearly  spher- 
ical. In  taking  them  up  we  shall  first  suppose  that  it  is  actually 
a  perfect  sphere,  and  then  later  consider  its  slight  deviations  from  the 
globular  form. 

The  simplest  and  most  certain  proof  of  the  globular  form  of 
the  earth  is  that  the  plane  of  the  horizon,  or  the  direction  of  the 
plumb  line,  changes  by  an  angle  which  is  directly  proportional  to 
the  distance  traveled  along  the  surface  of  the  earth,  whatever  be 
the  starting  point,  direction  of  travel,  and  distance  traveled.  This 
statement  needs  some  amplification.  Let  us  suppose  first  that  the 
earth  is  a  sphere  and  show  that  the  statement  is  true. 

In  Fig.  1,  let  the  circle  represent  the  earth  whose  center  is  at 
C,  and  let  us  suppose  that  the  stars  are  very  far  away  from  it  com- 
pared to  its  size.  Suppose  the  line  CP  points  to  the  pole  of  the  sky. 
Suppose  an  observer  is  at  0^  He  will  observe  the  pole  in  the  direc- 
tion Ofi,  which  is  parallel  to  CP  if  the  stars  are  supposed  to  be 
infinitely  far  away  compared  to  the  size  of  the  earth.  The  plane  of 
his  horizon  is  HI.  If  he  stands  at  Ol  and  looks  north  he  will  look 
in  the  direction  HI.  The  angle  between  the  plane  of  the  horizon  to 
the  north  and  the  line  from  the  observer  to  the  pole  is  al8 

Now  let  us  suppose  he  travels  northward  to  point  02.  Then 
the  direction  to  the  pole  becomes  02P2>  which  is  again  parallel  to 
CP.  His  horizon  in  this  case  is  H2.  The  distance  of  the  pole  above 


ASTRONOMY 


9 


the  horizon  is  now  the  angle  a2.  He  has  gone  along  the  surface  the 
distance  0^0^,  which  subtends  the  angle  OL  at  the  center  of  the  earth. 
We  wish  to  prove  that  the  direction  of  his  horizon  is  changed  by  the 
same  angle.  This  follows  at  once  because  the  lines  HI  and  H2  in 
the  figure  are,  respectively,  perpendicular  to  COi  and  C02,  and  there- 
fore by  plane  geometry  the  angle  between  Hl  and  Hz  is  equal  to  the 
angle  between  CO!  and  C02;  that  is,  the  change  of  direction  of  the 
horizon  is  equal  to  the  angular 
distance  the  observer  has  trav- 
eled along  the  surface  of  the 
earth.  If  the  earth  is  spherical, 
the  actual  distance  along  the 
surface  in  miles  is  proportional 
to  the  angle  subtended  at  the 
center.  Consequently,  the  orig- 
inal proposition  is  verified. 

There  is  no  other  figure 
than  the  sphere  for  which  the 
plane  of  the  horizon  will  change 
proportionately  to  the  distance 
traveled.  Consequently,  if  it 
is  found  that  as  one  travels 
over  the  surface  of  the  earth 

the  change  in  direction  of  the  plane  of  the  horizon  is  in  direct 
proportion  to  the  distance  he  travels,  it  proves  that  the  earth 
is  an  exact  sphere.  In  Fig.  1,  the  question  was  considered  only  for 
a  motion  north  and  south.  The  reason  for  this  was  that  the  north 
star  remains  fixed  in  the  sky  while  the  other  stars  appear  to  move 
around  the  earth  in  diurnal  circles  just  as  the  sun  and  moon  do. 
Therefore,  it  is  simpler  actually  to  make  the  observations  for  north- 
ward and  southward  motion,  and  it  is  also  easier  to  understand  the 
matter.  However,  in  order  to  show  that  the  earth's  curvature  is 
the  same  in  every  direction,  it  is  necessary  to  prove  the  proposition 
in  the  general  form  given  at  the  beginning. 

That  this  is  the  simplest  method  of  proving  the  shape  of  the 
earth  is  supported  by  the  fact  that  it  was  the  one  first  discovered 
and  used.  The  Greek  astronomer,  Eratosthenes,  more  than  two 
hundred  years  B.C.,  noticed  that  the  north  star  appeared  to  be  higher 


10 


ASTRONOMY 


when  he  was  in  Greece  than  it  did  during  his  journeys  farther  south 
in  Upper  Egypt.  f,  .He  correctly  interpreted  this  as  meaning  that 
the  earth  was  convex,  and  he  assumed  it  was  spherical.  In  fact,  he 
went  so  far  as  to  try  to  find  the  size  of  the  earth  by  measuring  the 
distance  he  had  to  travel  over  its  surface  to  cause  the  pole  star  to 
change  its  elevation  above  the  horizon  by  one  degree.  While  at 
that  very  early  date  correct  ideas  of  the  shape  of  the  earth  were 
entertained  by  a  few  and  attempts  were  actually  made  to  find  its 
size,  nevertheless  the  belief  in  the  roundness  of  the  earth  perished 
because  of  the  lack  of  the  scientific  spirit  and  the  mysticism  of  antiq- 
uity. There  was  no  general  acceptance  of  the  fact  that  the  earth  is 
round  until  after  Columbus  had  crossed  the  Atlantic  and  his  imme- 
diate followers  had  circumnavi- 
gated the  globe. 

Oblateness  of  the  Earth.  In 
the  preceding  section  a  method 
of  proving  the  sphericity  of  the 
earth  was  given,  providing  the 
earth  were  actually  spherical.  If 
it  is  not  perfectly  round,  obvi- 
ously the  method  ought  to  reveal 
this  fact.  As  a  matter  of  fact  it 
has  been  found  that  the  earth  is 
slightly  flattened  at  the  poles  and 
bulged  at  the  equator.  We  shall 
now  see  how  the  observations 
have  shown  this  to  be  true. 
Let  us  first  suppose  that  the  earth  is  flattened,  as  has  been  stated, 
and  see  what  the  observation  should  show.  In  Fig.  2,  let  the  curve 
E  represent  a  section  of  the  earth  through  its  axis  and  perpendicular 
to  its  equator.  Let  the  circle  Ci  be  a  circle  which  has  the  same  curva- 
ture as  the  earth  at  its  equator,  and  let  the  circle  C2  be  that  one 
which  has  the  same  curvature  as  the  earth  at  its  pole.  It  is  clear 
from  the  figure  that  d  is  smaller  than  (72.  Consequently,  if  one  were 
to  go  a  degree  north  or  south  on  the  earth  at  its  equator  he  would  be 
going  a  distance  equal  to  one  degree  on  the  circle  Clt  and  if  he  were 
to  go  a  degree  north  or  south  on  the  earth  near  the  pole  he  would  be 
going  a  distance  equal  to  one  degree  on  the  circle  (72;  that  is,  a  dis- 


Fig.  2.  The  Curve  E  Is  a  Section  of  the  Flat- 
tened Earth;  C\  Is  a  Circle  Having  the  Curva- 
ture of  the  Earth  at  Its  Equator,  and  C2  One 
Having  the  Curvature  of  the  Earth  at  Its  Pole 


ASTRONOMY  11 

tance  corresponding  to  one  degree  as  measured  by  the  difference  in 
direction  of  the  pole  is  less  at  the  equator  of  the  earth  than  it  is  at 
the  pole  of  the  earth  if  the  earth  is  flattened.  On  the  other  hand, 
if  the  earth  were  elongated  in  the  direction  of  its  axis  the  opposite 
result  would  be  true. 

The  actual  shape  of  the  earth  was  under  discussion  for  a  long 
time,  the  English,  following  Newton,  taking  the  position  that  it  is 
flattened  at  the  poles  and  bulged  at  the  equator;  and  the  French, 
who  were  generally  opposed  to  the  English  in  everything,  taking 
the  position  that  it  is  flattened  at  the  equator  and  bulged  at  the 
poles.  About  1745  the  French  measured  an  arc  in  Lapland  near  the 
Arctic  Circle,  and  another  in  Peru  near  the  equator.  They  found 
definitely  that  the  arc  one  degree  in  length  was  longer  in  Lapland 
than  it  was  in  Peru.  This  proved  beyond  any  question  that  the 
earth  is  flattened  at  the  poles  and  bulged 
at  the  equator,  and  besides  it  gave  the 
amount  of  the  flattening. 

Newton's  prediction  that  the  earth 
would  be  found  by  observations  to  be 
oblate  is  one  worthy  of  notice.  Relying 
on  the  fact  that  the  earth  rotates  he  was 
able  to  prove  it.  In  Fig.  3,  let  PP'  be 
the  axis  around  which  the  earth  rotates, 
and  Q  a  point  on  its  equator.  Newton  rig.  s.  Newton's  Canal  Proof 

,  ,  i    P  -r»  That  the  Earth  Is  Oblate 

imagined  a  canal  constructed  from  P  to 

(7,  the  center  of  the  earth,  and  then  from  C  to  Q.  The  rotation  of 
the  earth  has  no  effect  upon  the  weight  of  the  water  in  the  canal 
PC.  But  the  rotation  decreases  the  weight  of  every  unit  volume 
of  water  in  the  canal  CQ,  the  amount  of  the  decrease  depending  on 
its  distance  from  the  axis.  Now,  if  the  two  canals  are  to  be  in 
equilibrium  the  pressure  of  PC  at  C  must  be  exactly  equal  to  the 
pressure  of  QC  at  C.  Since  each  unit  volume  in  QC  exerts  a  less 
pressure  than  the  corresponding  one  in  PC,  it  follows  that  the  canal 
QC  must  be  longer  than  the  canal  PC.  It  is  not  a  simple  matter  to 
find  how  much  longer  it  must  be,  yet  Newton  solved  the  problem 
and  his  results  have  been  verified. 

There  is  a  third  method  of  proving  the  existence  of  the  equa- 
torial bulge  of  the  earth.    The  moon  is  kept  in  its  orbit  around  the 


12 


ASTRONOMY 


Fig.  4.    The  Moon's  Attraction  for 

the  Equatorial  Bulge  of  the  Earth 

fleets  Rotation  and  Proves 

That  There  Is  a  Bulge 


earth  by  the  earth's  attraction  for  it.  Now,  the  attraction  of  the 
earth  on  the  moon  is  not  quite  the  same  if  it  is  oblate  as  it  would  be 
if  it  were  strictly  spherical.  This  variation  in  attraction  will  cause 
a  corresponding  small  change  in  the  motion  of  the  moon.  When  the 
amount  of  the  equatorial  bulge  is  known,  the  irregularities  produced 
by  it  on  the  motion  of  the  moon  can  be  computed.  As  a  matter  of 

fact  they  have  been  computed  and  it  has 
been  found  that  the  motion  of  the  moon 
has  exactly  those  irregularities  which  it 
should  have  if  the  earth  were  oblate,  thus 
verifying  the  fact  of  its  oblateness. 

Conversely,  the  attraction  of  the  moon 
for  the  earth  is  different  from  what  it 
would  be  if  the  earth  were  spherical. 

In  Fig.  4,  let  E  represent  the  largest 
sphere  which  can  be  cut  out  of  the  flat- 
tened earth.  The  attraction  of  the  moon 

has  no  effect  on  the  rotation  of  the  sphere,  but  its  attraction  on  the 
equatorial  bulge,  A  and  B,  does  have  an  effect  upon  the  rotation  of 
the  earth.  This  effect  is  actually  observed  and  proves  that  the  earth 
is  bulged  at  the  equator.  Not  only  do  all  these  proofs  agree  in 
showing  that  it  is  oblate,  but  they  also  agree  in  the  determination 
of  the  amount  of  the  oblateness. 

It  is  not  sufficient  to  say  that  the  earth  is  flattened  at  the  poles 
and  bulged  at  the  equator,  but  it  is  necessary  to  describe  more  exactly 

its  form.  In  order  to  do  this  we  must 
define  the  curve  called  an  ellipse,  which 
is  represented  in  Fig.  5. 

The  ellipse  is  an  oblong,  closed  curve, 
such  that  the  sum  of  the  distances  from 
two  fixed  points  within,  F  and  F',  to  any 
point  P  on  its  circumference  is  always  the 
AreipAnd^'hich  '  same-  Jt  follows  from  this  definition  that 
a  convenient  way  to  draw  it  is  to  set  two 

pins  at  F  and  F'  in  the  drawing-board  and  to  tie  the  ends  of  a  string, 
whose  length  is  somewhat  greater  than  the  distance  FF',  to  them. 
Then  if  a  pencil  is  put  in  the  string  at  P  and  held  tight,  the  circum- 
ference of  the  ellipse  can  be  easily  traced  out. 


ASTRONOMY 


13 


If  the  ellipse  be  rotated  around  the  diameter  BB'  it  generates 
a  solid  which  is  called  an  oblate  spheroid.  Its  shape  is  roughly  like 
that  of  an  orange.  If  it  were  rotated  around  the  longest  axis,  A  A', 
it  would  generate  what  is  called  a  prolate  spheroid,  whose  shape  is 
similar  to  that  of  a  long  watermelon.  Now,  the  shape  of  the  earth 
is  very  nearly  that  of  an  oblate  spheroid,  though  the  amount  of 
flattening  is  so  small  that  if  it  were  drawn  to  scale  it  would  appear  to 
the  eye  as  sensibly  spherical.  There  are  some  slight  deviations  from 
the  oblate  spheroidal  figure  due  principally  to  the  continental  eleva- 
tions and  the  irregularities  in  the  distribution  of  matter. 

Size  of  the  Earth.  The  measurements  of  the  arcs  on  the 
surface  of  the  earth  not  only  prove  its  shape  but  furnish  us  directly 
its  size.  It  has  been  found  in  this  way  that  its  mean  diameter  is 
about  7,910  miles.  The  equatorial  dia- 
meter is  about  27  miles  greater  than  the 
polar,  owing  to  the  flattening  of  the  earth. 
According  to  the  most  accurate  observa- 
tions and  computations  so  far  made,  the 
equatorial  diameter  is  7,926.7  miles,  and 
the  polar  diameter  7,900  miles.  Accord- 
ing to  this  the  equatorial  circumference 
of  the  earth  is  24,902  miles. 

From  the  figures  given  above  it  is 
found   that   one   degree   in  latitude   at 

the  earth's  equator  equals  68.7  miles,  and  at  the  pole,  69.4  miles; 
that  is,  a  degree  at  the  pole  is  about  one  per  cent  longer  than  one 
at  the  equator.  In  longitude,  one  degree  at  the  equator  equals 
69.7  miles.  In  latitude  forty  degrees,  one  degree  in  longitude 
equals  53.4  miles.  In  latitude  sixty  degrees,  one  degree  in  longitude 
equals  34.9  miles  and,  of  course,  at  the  pole  there  is  no  such  thing  as 
longitude. 

Different  Kinds  of  Latitude.  Since  the  earth  is  not  a  perfect 
sphere,  a  perpendicular  to  its  surface  (i.e.,  water  level  surface),  at 
any  point  except  on  the  equator  or  at  the  poles  does  not  pass  through 
its  center.  This  gives  rise  to  different  kinds  of  latitude. 

In  Fig.  6,  let  P  represent  the  pole  of  the  earth,  E  a  point  on  its 
equator,  and  C  its  center.  Suppose  an  observer  is  at  0  and  that  OA 
is  perpendicular  to  the  surface  at  0.  The  geocentric  latitude  is  the 


Fig.  6. 
Is  a 


The  Geocentric  Latitude 
and  the  Astronomical 
Latitude  Is  a<i 


14  ASTRONOMY 

angle  ECO  =  a1.  The  astronomical  latitude,  i.e.,  the  latitude  which 
would  be  found  by  astronomical  observations,  is  the  angle  a2.  It 
is  seen  from  the  figure  that  the  astronomical  latitude  is  a  little  greater 
than  the  geocentric  latitude. 

Density  of  the  Earth.  In  measuring  the  densities  of  solids  and 
liquids  it  is  customary  to  use  water  at  its  greatest  density  as 
the  standard.  It  is  necessary  to  state  that  the  density  of  water 
at  a  given  temperature  is  used  as  the  standard  because  it  varies 
with  the  temperature.  If  we  start  with  a  very  high  temperature 
the  density  increases  as  the  temperature  falls  until  it  reaches  about 
39°  F.,  after  which  the  density  begins  to  decrease.  If  this  were  not 
so,  ice  would  be  denser  than  water  and  would  sink  instead  of  float. 
When  it  is  said  that  the  density  of  rock  is  three,  it  is  meant  that 
a  given  volume  of  rock  weighs  three  times  as  much  as  the  same 
volume  of  water  at  its  greatest  density. 

It  is  a  simple  matter  to  determine  by  direct  examination  the 
densities  of  those  materials  on  the  earth  which  are  so  near  its  surface 
they  can  be  actually  reached.  But  when  it  is  understood  that  the 
deepest  borings  in  the  earth  reach  to  a  depth  of  about  two  miles 
only,  which  is  only  ToW  of  the  distance  to  the  earth's  center,  it  is 
clear  how  small  a  part  of  the  earth's  mass  comes  directly  under  our 
observation.  It  is,  therefore,  necessary  to  discover  some  indirect 
method  of  finding  the  density  of  those  parts  which  lie  so  deep  we 
can  not  reach  them. 

The  volume  of  the  earth  being  known,  its  density  can  be  found 
provided  we  can  discover  some  way  of  finding  its  mass.  The  masses 
of  all  astronomical  bodies  are  found  by  their  attractions  for  known 
bodies.  The  attraction  of  the  earth  for  masses  at  its  surface  is  what 
gives  them  weight.  It  is  possible,  though  it  is  a  very  delicate  experi- 
ment, to  compare  the  attraction  of  the  earth  for  a  small  ball  with  that 
of  a  large  ball  for  the  same  small  one.  The  delicacy  of  the  experi- 
ment comes  from  the  fact  that  the  force  of  gravity  is  so  feeble  that 
it  is  with  great  difficulty  that  the  attraction  of  the  large  ball  for  the 
small  one  can  be  measured.  Let  us  suppose,  however,  that  it  has 
been  measured,  as  is  actually  the  case  in  many  experiments  which 
have  been  carried  out,  and  let  us  see  how  the  mass  of  the  earth  can 
be  determined.  The  attraction  of  one  body  for  another  depends 
upon  two  chief  factors,  viz,  the  mass  of  the  attracting  body  and 


ASTRONOMY  15 

its  distance  from  the  attracted  body.  Now,  in  the  experiment  of 
comparing  the  attraction  of  the  earth  with  that  of  a  large  ball  for 
a  small  ball,  the  distances  of  the  earth  and  the  large  ball  from  the 
small  one  are  known.  The  relative  attractions  are  measured.  The 
density  of  the  large  ball  and,  therefore,  its  mass  are  known.  The 
only  unknown  in  the  proportion  is  the  mass  of  the  earth;  or,  since 
its  volume  is  known,  the  only  unknown  is  its  density.  By  means 
of  these  measurements  and  the  discussion  of  them,  it  has  been  found 
that  the  average  density  of  the  earth  taken  through  and  through 
is  about  5.5.  The  average  density  of  the  surface  rock  with  which 
we  are  familiar  is  from  2.75  to  3.  This  means  that  the  interior  is, 
on  the  whole,  considerably  denser  than  the  surface  rock.  Two 
explanations  of  this  are  possible:  First,  the  material  of  which  the 
interior  is  composed  may  be  largely  of  dense  substances;  second, 
it  may  be  that  the  great  pressures  which  prevail  in  the  interior  are 
sufficient  to  squeeze  ordinary  matter  to  such  an  extent  that  its 
density  is  increased  enough  to  account  for  the  greater  density  of  the 
interior. 

The  pressure  on  the  interior  of  the  earth  is  enormous.  The 
weight  of  a  cubic  foot  of  water  is,  in  round  numbers,  60  pounds,  and 
of  the  surface  rock  approximately  180  pounds.  If  we  stretch  this 
cube  out  into  a  parallelepiped,  whose  base  is  one  inch  square,  its 
height  will  be  1,728  inches  (since  there  are  1,728  cubic  inches  in  a 
cubic  foot),  or  144  feet.  The  pressure  of  this  column  on  its  base 
will  be  its  weight  of  180  pounds.  The  pressure  on  such  a  column  of 
one-inch  cross-section  at  the  depth  of  one  mile  will  be  \W  X 180  = 
6,600  pounds.  The  pressure  at  the  depth  of  100  miles,  therefore,  will 
equal  330  tons  per  square  inch,  which  is  a  very  moderate  depth 
when  the  earth  as  a  whole  is  considered.  It  is  [easily  conceivable 
that  these  enormous  pressures  are  sufficient  to  give  ordinary  matter 
a  density  of  5.5,  and  consequently  there  is  no  reason  to  believe  from 
these  considerations  that  the  material  of  which  the  interior  of  the 
earth  is  made  is,  on  the  whole,  radically  different  from  that  which  is 
near  its  surface. 

Condition  of  Interior  of  the  Earth.  It  has  been  very  generally 
believed  until  recent  times  that  the  interior  of  the  earth  is  in  a  fluid 
state,  owing  to  the  high  temperatures  prevailing  there.  It  has  been 
found  that  the  temperature  rises  about  1°  F.  for  every  50  to  100  feet 


16  ASTRONOMY 

that  one  goes  down  in  the  earth.  The  rate  of  increase  of  temperature 
varies  greatly  at  different  places.  But  taking  the  slowest  rate 
observed,  it  is  seen  that  if  it  continues  to  great  depths  the  temperature 
of  the  interior  must  be  very  high.  Suppose,  for  example,  that  the 
increase  of  temperature  is  only  one  degree  for  100  feet.  Then  the 
increase  of  temperature  at  the  depth  of  a  mile  would  be  50  degrees. 
At  the  very  moderate  depth  of  100  miles  we  should  find  a  temperature 
of  5,000  degrees,  which  would  not  only  liquefy  but  vaporize  most 
substances.  It  has  been  inferred  from  this  that  the  interior  is  in  a 
molten  state,  which  has  been  further  proved  by  the  expulsion  of 
melted  rock  material  from  volcanoes,  these  having  been  interpreted 
as  cracks  through  the  solid  crust  covering  the  fluid  interior. 

In  these  conclusions  regarding  the  condition  of  the  interior  of 
the  earth  a  very  important  factor  has  been  neglected.  It  was 
remarked  above  that  the  pressure  at  moderate  depths  in  the  earth  is 
very  high  indeed.  Now  pressure  tends  to  keep  matter  in  a  solid 
state  in  spite  of  high  temperature.  That  is,  if  a  temperature  of  2,000 
degrees  will  melt  a  substance  at  ordinary  atmospheric  pressure,  a 
temperature  of  3,000  degrees  might  be  required  to  melt  it  if  it  were 
subject  to  a  great  pressure.  While  the  combination  of  such  extremely 
high  pressures  and  temperatures  as  prevail  in  the  interior  of  the 
earth  have  not  been  realized  in  experiments,  still  there  is  room  for 
doubt  as  to  the  conclusion  regarding  the  fluidity  of  the  interior  of 
the  earth.  The  effects  of  pressure  in  retarding  the  melting  are  similar 
to  those  of  raising  the  boiling  points  of  liquids.  At  the  sea  level 
under  ordinary  atmospheric  pressure,  water  boils  at  212°  F.,  but  on 
the  tops  of  high  mountains  where  the  pressure  is  perhaps  25  per 
cent  less,  the  boiling  point  is  considerably  lower.  This  leads  to  the 
well-known  fact  that  water  boils  away  rapidly  on  the  mountains, 
and  that  things  to  be  cooked  by  boiling  are  cooked  only  with 
difficulty,  the  reason  being  that  sufficiently  high  temperatures  are 
not  obtainable. 

There  are  now  definite  reasons  for  believing  that  the  earth  is 
solid  through  and  through,  and  one  of  them  is  that  the  earthquake 
waves  are  transmitted  as  they  would  be  if  it  were  a  solid.  The  speed 
with  which  a  wave  travels  through  any  medium,  for  example,  the 
wave  produced  by  striking  a  steel  beam  with  a  heavy  hammer, 
depends  upon  the  density  of  the  medium  and  its  rigidity.  Earth- 


ASTRONOMY  17 

quakes  are  similar  waves  in  the  earth.  We  now  have  very  delicate 
instruments  for  measuring  them,  even  at  those  remote  distances 
from  the  seat  of  disturbance  where  they  have  become  very  small. 
Suppose  an  earthquake  starts  in  Japan,  where  many  of  them  do  start, 
and  that  it  is  of  such  intensity  that  the  waves  can  be  detected  when 
they  reach  Europe  and  America.  We  shall  suppose  the  time  of  the 
earthquake  in  Japan  has  been  recorded,  and  that  the  time  the  wave 
reached  Europe  and  America  has  also  been  recorded.  The  distance 
and  the  time  it  has  taken  the  wave  to  travel  from  one  place  to  the 
other  being  known,  it  is  possible  to  compute  the  speed  of  the  wave. 
Now,  as  has  just  been  stated,  the  speed  depends  upon  the  density  and 
the  rigidity  of  the  medium  through  which  the  waves  pass.  In  the 
case  of  the  earth  the  density  is  known,  as  we  have  shown  above. 
Consequently,  the  only  unknown  is  the  rigidity  of  the  earth,  which 
from  these  observations  turns  out  to  be,  on  the  average,  considering 
the  earth  through  and  through,  about  that  of  steel. 

There  are  other  methods  of  determining  the  rigidity  of  the  earth, 
and  they  lead  to  the  same  results.  One  of  them  is  the  tides  that  the 
moon  raises  in  the  earth.  It  can  be  shown  from  a  mathematical 
discussion  of  the  question  that  if  the  earth  had  a  thin  crust,  say  100 
miles  in  depth,  and  a  fluid  interior,  then  this  crust  would  yield  under 
the  tidal  force  so  the  water  on  its  surface  would  not  be  heaped  up  in 
tides.  It  is  clear  that  if  the  crust  yielded  there  would  be  no  reason 
for  the  water  to  flow  along  it  under  the  tidal  forces.  Now,  it  is  found 
by  observations  that  the  tides  are  the  height  they  should  be  if  the 
solid  part  of  the  earth  had  a  very  high  degree  of  rigidity.  That  is,  the 
tidal  phenomena  in  connection  with  a  difficult  mathematical  theory 
prove  that  the  earth  is  rigid  when  considered  in  its  entirety. 

It  was  stated  above  that  the  moon's  attraction  on  the  equatorial 
bulge  of  the  earth  produced  changes  in  its  rotation.  If  the  interior 
of  the  earth  were  fluid,  so  that  the  equatorial  bulge  could  slip  on  the 
interior,  then  the  attraction  of  the  moon  for  it  would  produce  more 
rapid  changes  in  the  motion  of  the  interior  of  the  earth  than  it  would 
if  the  equatorial  bulge  were  solidly  attached  to  the  whole  earth  so 
that  the  moon  would  have  to  move  all  of  it.  It  is  possible  to  compute 
the  rate  of  change  under  the  hypothesis  that  the  earth  is  a  solid  and 
also  under  the  hypothesis  that  the  equatorial  bulge  can  slip  on  the 
interior.  It  is  found  from  the  actual  observations  that  the  rate  of 


18  ASTRONOMY 

change  is  just  what  it  should  be  if  the  earth  were  solid  through  and 
through.  The  conclusion  to  be  drawn  from  this  line  of  reasoning  is 
that  the  earth  is  not  only  solid  but  that  it  has  a  rigidity  about  equal 
to  that  of  steel. 

There  are  other  indirect  methods  of  treating  the  question  and 
they  all  lead  to  the  same  conclusion.  The  fact  that  the  earth  is  solid 
in  the  interior — when  a  more  superficial  examination  of  the  question 
would  lead  to  the  conclusion  that  it  is  fluid — is  of  the  highest  interest. 
It  is  clear  that  this  is  a  very  important  result  for  the  geologist.  It  is 
interesting  from  the  scientific  point  of  view  that  we  have  been  able 
to  reach  certain  conclusions  respecting  portions  of  the  earth  which 
can  never  directly  come  under  our  observations.  It  is  one  of  the 
triumphs  of  science  that,  through  the  application  of  laws  which  are 
discovered  in  treating  material  which  is  accessible  to  us,  we  can  dis- 
cover the  properties  of  that  which  is  inaccessible. 

Composition  of  the  Earth's  Atmosphere.  The  atmosphere  is 
the  gaseous  envelope  which  surrounds 'the  earth.  It  is  made  up  of 
nitrogen  and  oxygen  and  a  few  other  substances.  The  thousands 
of  substances  which  are  found  on  and  in  the  earth  are  made  up  of 
about  eighty  fundamental  substances  called  elements.  For  example, 
water  is  a  combination  of  the  elements  oxygen  and  hydrogen,  and 
sugar  is  a  more  complicated  combination  of  carbon,  oxygen,  and 
hydrogen. 

Of  the  earth's  atmosphere  about  79  per  cent  is  nitrogen,  about 
21  per  cent  is  oxygen,  and  in  addition  there  are  very  minute  quan- 
tities of  other  elements  such  as  argon,  neon,  and  helium,  and  some 
compounds  such  as  carbon  dioxide  and  water  vapor.  Carbon  dioxide 
is  a  compound  made  up  of  carbon  and  oxygen,  and  is  produced  by 
the  combustion  of  coal,  wood,  and  most  other  substances. 

Height  of  the  Earth's  Atmosphere.  It  is  found  upon  ascending 
mountains  or  going  up  in  balloons  that  the  density  of  the  atmosphere 
steadily  decreases  with  increasing  altitude.  Numerous  observations 
in  various  places  on  the  earth  and  at  various  times  have  shown  that 
at  a  height  of  three  and  a  half  miles  above  the  surface  of  the  earth 
the  density  is  approximately  one-half  that  at  the  surface.  It  is 
also  found  from  balloon  ascensions  that  an  ascent  of  three  and  a  half 
miles  more  reaches  a  place  where  the  density  of  the  atmosphere  is 
one-half  of  that  at  the  three  and  a  half  mile  level,  or  one  fourth  that 


ASTRONOMY  19 

at  the  surface  of  the  earth.  So  far  as  it  has  been  possible  to  extend 
the  observations,  the  density  of  the  atmosphere  is  divided  by  two  for 
every  three  and  a  half  miles  of  ascent.  If  this  law  were  indefinitely 
continued  the  atmosphere  would,  of  course,  have  infinite  extent, 
though  the  density  would  become  very  low  after  a  few  miles.  For 
example,  the  density  at  the  height  of  28  miles  would  be  only  -5-^  that 
at  the  earth's  surface. 

It  is  not  possible  to  determine  by  any  means  whatever  exactly 
where  the  earth's  atmosphere  ceases.  In  discussing  its  height  we 
can  refer,  therefore,  only  to  the  height  to  which  it  extends  in  sensi- 
ble quantities.  Clouds  do  not  reach  an  altitude  above  10  or  12 

_A 

miles,  and  balloons  have  not  been  sent  higher  than  that.  There- 
fore, for  the  purpose  of  carrying  water  vapor  and  balloons  we 
might  say  its  height  is  approximately  12  miles.  But  there  are 
other  phenomena  which  do  not  require  so  dense  an  atmosphere  for 
their  existence. 

A  very  good  means  of  determining  the  height  of  the  atmosphere 
is  from  the  observations  of  meteors.  These  little  flashes  of  light  in 
the  sky,  which  are  commonly  called  shooting  stars,  are  due  to  minute 
masses  of  matter,  traveling  in  the  interplanetary  spaces,  which  are 
entirely  invisible  until  they  dash  into  the  earth's  atmosphere.  They 
travel  with  very  high  speed,  even  as  great  as  twenty  or  thirty  miles 
per  second,  and  the  friction  they  encounter  in  striking  the  atmos- 
phere generates  so  great  a  heat  that  they  become  luminous.  As  they 
are  burned  up  and  their  motion  is  destroyed  the  incandescent 
particles  associated  with  them  cool  off  and  they  become  invisible. 
Now,  it  is  possible  by  direct  observations  to  find  the  height  at  which 
meteors  burn. 

In  Fig.  7,  suppose  there  is  an  observer  on  the  surface  of  the 
earth  at  A  and  another  a  few  miles  distant  at  B,  and  suppose  a 
meteor  strikes  the  atmosphere  at  m.  The  observer  at  A  will  see  it 
at  an  angular  elevation  of  a  and  the  observer  at  B  at  an  angular 
elevation  of  b.  When  these  angles  have  been  measured  and  the 
distance  from  A  to  B  is  known,  it  is  possible  to  compute  the  height 
of  m  above  the  surface  of  the  earth.  The  computation  is  made  by 
trigonometry,  but  one  can  get  fairly  accurate  results  without  the 
use  of  it.  On  drawing  paper  the  distance  A  and  B  can  be  laid  down 
to  any  convenient  scale  and  the  angles  a  and  b  laid  off.  The  place 


20 


ASTRONOMY 


where  the  lines  intersect  will  be  the  point  m.  The  distance  from  m 
to  the  line  AB  can  be  measured  directly  by  a  ruler,  and  it  can  be 
found  in  this  way  how  the  height  of  a  meteor  is  related  to  the  dis- 


Fig.  7.     The  Height  of  the  Meteor  m  Can  Be  Determined  by 
Observations  from  A  and  B 

tance  of  A  from  B.  Many  observations  of  this  sort  have  shown  us 
that  the  atmosphere  is  sufficiently  dense  to  an  altitude  of  about  100 
miles  to  cause  the  meteors  to  burn  when  they  strike  into  it.  Nearly 
all  of  them  are  totally  consumed  before  they  reach  an  altitude  of 
50  miles. 

Another  phenomenon  which  depends  upon  the  height  of  the 
atmosphere  and  by  means  of  which  we  can  compute  its  height  is 
the  twilight. 

In  Fig.  8,  suppose  the  sun  is  very  far  to  the  left  and  shines 
toward  the  right,  its  rays  striking  the  earth  in  sensibly  parallel  lines. 
For  an  observer  at  the  point  P  the  sun  is  on  the  horizon.  Suppose, 


Fig.  8.     An  Observer  at  0  Sees  the  Twilight  at  Q  Until  the  Sun  Is 

Far  Below  the  Horizon.      From  the  Duration  of  the  Twilight 

the  Height  of  the  Atmosphere  Can  Be  Found 

for  example,  it  is  setting.  For  an  observer  at  0  the  sun  has  been 
down  some  time,  depending  upon  the  distance  from  0  to  P.  The 
horizon  of  the  observer  at  0  is  indicated  by  the  line  H.  Now,  it  is 


ASTRONOMY  21 

clear  from  the  diagram  that  some  of  the  atmosphere  which  is  above 
H,  viz,  that  at  Q,  is  illuminated  by  the  rays  of  the  sun.  Conse- 
quently, the  observer  at  0,  looking  toward  his  western  horizon,  will 
see  the  atmosphere  somewhat  illuminated.  It  is  also  clear  from  the 
diagram  that  the  length  of  time  the  illumination  will  be  visible  in 
the  west  depends  upon  the  height  of  the  atmosphere.  The  higher 
the  atmosphere  the  longer  it  can  be  seen.  Actual  observation  shows 
that  the  twilight  lasts  until  the  sun  is  15  to  20  degrees  below  the 
horizon.  When  the  matter  is  discussed  mathematically  this  proves 
that  the  atmosphere  is  dense  enough  to  an  altitude  of  40  to  60  miles 
to  produce  the  twilight  phenomena. 

Another  means  of  determining  the  height  of  the  atmosphere  is 
by  the  aurora,  a  phenomenon  on  which  is  now  well  understood  to 
be  an  electrical  display  in  the  rare  gases  of  the  high  upper  atmos- 
phere. Suppose  a  well-defined  auroral  streamer  is  observed  from 
two  places  at  the  same  time.  Then,  as  in  the  case  of  computing 
the  height  of  the  meteor  when  it  becomes  visible,  the  height  of  the 
auroral  streamer  can  be  computed.  Observations  of  this  phenomenon 
have  shown  that  the  auroral  light  is  visible  to  a  height  sometimes  as 
great  as  400  miles. 

It  is  seen  that  the  various  methods  of  determining  the  height 
of  the  observer  do  not  agree,  and  the  reasons  for  their  disagreement 
are  plain.  They  are  not  in  harmony  because  each  one  determines 
where  the  atmosphere  ceases  to  be  dense  enough  to  produce  the 
particular  phenomenon  in  question.  Speaking  from  a  practical  stand- 
point, we  may  say  that  sensibly  all  of  the  earth's  atmosphere  is 
within  100  miles  of  its  surface. 

In  considering  the  mass  of  the  earth  one  might  at  first  think  it 
is  inappropriate  to  consider  the  atmosphere  as  a  part  of  it,  but  upon 
a  little  reflection  it  is  apparent  that  the  atmosphere  is  as  much  a 
part  of  the  earth  as  the  water  which  covers  a  large  part  of  its 
surface,  or  as  the  solid  part  itself.  Taking  into  account  the  density 
and  extent  of  the  atmosphere,  it  is  found  that  altogether  it  is  about 
mftmr  that  of  the  remainder  of  the  earth. 

Kinetic  Theory  of  Gases.  For  certain  discussions  it  is  essential 
to  have  a  clear  idea  of  the  nature  of  a  gas.  It  has  been  stated 
above  that  the  atmosphere  is  made  up  of  a  few  elements  and  com- 
pounds in  the  gaseous  state.  These  masses  are  composed  of  vast 


22  ASTRONOMY 

numbers  of  extremely  small  particles  called  molecules.  In  fact  every 
substance,  whether  it  is  an  element  or  a  compound,  is  made  up  of 
small  particles  called  molecules.  When  an  object  is  in  the  solid  state 
its  molecules  are  fixed  relatively  to  one  another.  If  this  were  not 
so  a  solid  body  would  not  preserve  its  shape.  While  it  is  true  that 
they  are  fixed  to  the  extent  that  they  do  not  move  around  among 
one  another,  they,  nevertheless,  have  slight  oscillatory  motions. 

In  the  case  of  a  liquid  the  molecules  not  only  oscillate  but  move 
around  among  one  another.  If  two  liquids  of  the  same  density  but 
of  different  colors  be  put  together  it  will  be  seen  they  gradually 
mix  completely  because  of  this  fact.  WThile  the  molecules  move 
around  among  one  another  in  the  case  of  liquids,  they,  nevertheless, 
do  not  move  freely  because  they  are  so  close  together  that  each  one 
is  continually  subject  to  restraints  from  the  neighboring  ones. 

In  the  case  of  a  gas  the  molecules  are  far  apart  compared  to 
their  size,  and  they  dart  around  in  every  direction  with  great  speed. 
The  collisions  of  the  molecules  are  extremely  frequent,  but  the  time 
that  one  is  sensibly  influenced  by  another  one  is  short  relatively  to 
the  time  between  collisions.  For  example,  if  a  molecule  makes  a 
million  collisions  in  a  second  it  might  be  that  it  would  be  sensibly 
disturbed  at  these  collisions  all  together  during  only  nrTroinnr  of 
a  second.  The  distinction  between  a  liquid  and  a  gas  is  that  in  the 
liquid  the  molecules  are  continually  subject  to  restraints  from 
neighboring  ones  while  in  a  gas  they  are  most  of  the  time  free. 

The  atmosphere  exerts  a  pressure  of  about  15  pounds  per  square 
inch  at  the  sea  level.  This  is  made  evident  by  exhausting  the  air 
from  a  reservoir  when  it  will  be  broken  unless  it  is  very  strong. 
This  pressure  is  produced  by  the  impact  of  countless  molecules  which 
strike  every  square  inch  millions  and  millions  of  times  per  second. 
The  individual  strokes  are  so  small  and  they  are  so  frequent  that 
the  pressure  is  sensibly  continuous.  From  the  density  of  the 
atmosphere  and  the  amount  of  pressure  which  it  exerts,  it  is  possible 
to  compute  the  average  speed  with  which  the  individual  molecules 
move.  Thus,  hydrogen  molecules  under  atmospheric  pressure  and  at 
the  freezing  point  move  on  the  average  with  a  velocity  of  more  than 
a  mile  a  second.  The  average  velocity  increases  with  the  increase 
of  temperature,  and  also  with  the  increase  of  pressure.  There  are 
many  molecules  moving  with  velocities  greater  than  the  average, 


ASTRONOMY  23 

and  many  with  velocities  less.  Theoretically  there  is  no  limit  to  the 
velocities  with  which  a  few  may  move.  The  higher  the  velocity  the 
fewer  the  molecules  which  will  be  moving  with  it. 

Escape  of  Atmospheres.  Suppose  a  body  is  projected  up  from 
the  surface  of  the  earth.  The  height  to  which  it  will  rise  depends 
upon  the  speed  with  which  it  is  started.  The  greater  the  speed  the 
higher  it  will  rise,  and  there  is  a  certain  definite  speed  for  which  it 
will  leave  the  earth  permanently.  It  is  found,  by  computation  based 
upon  the  mathematical  formulas  belonging  to  the  question,  that  if 
a  body  leaves  the  surface  of  the  earth  with  a  velocity  greater  than 
seven  miles  per  second  it  will,  except  for  the  resistance  of  the 
atmosphere,  leave  the  earth  and  never  return. 

Now,  let  us  apply  this  idea  to  the  molecules  of  the  atmosphere 
itself.  They  are  darting  to  and  fro  in  every  direction  with  high 
speeds,  the  velocities  in  some  cases  being  as  great  as  seven  miles 
per  second.  If  a  molecule  is  near  the  upper  limits  of  the  atmosphere 
where  the  chances  of  collision  are  growing  small,  and  if  it  darts  out 
away  from  the  earth  with  a  velocity  exceeding  seven  miles  per 
second,  it  will,  unless  it  strikes  another  molecule,  leave  the  earth 
permanently.  In  this  way  the  earth  is  probably  losing,  molecule  by 
molecule,  some  of  its  atmosphere. 

The  velocities  with  which  the  molecules  of  the  atmosphere  move 
depend  upon  their  individual  weights.  The  lightest  molecules  we 
know  are  those  of  hydrogen  which,  as  has  been  stated,  at  atmospheric 
pressure  and  at  the  freezing  point  move  with  a  velocity  greater  than 
one  mile  per  second.  The  molecules  which  our  atmosphere  is  largely 
made  of,  viz,  nitrogen  and  oxygen,  are,  respectively,  14  and  16  times 
heavier  than  hydrogen  and  move  on  the  average  with  about  one- 
fourth  the  velocity  of  hydrogen.  This  velocity  is  so  far  below  the 
seven  miles  per  second  necessary  for  escape  from  the  earth  that  it 
is  clear  there  is  no  great  danger  of  the  atmosphere  escaping  rapidly. 
Nevertheless,  there  is  indefinite  time  available  for  its  escape  and 
there  might  be  a  danger  of  its  being  seriously  depleted  in  this 
manner. 

Before  drawing  definitely  the  conclusion  that  the  earth  is  losing 
its  atmosphere  and  that.it  is  continually  becoming  more  tenuous, 
we  should  see  whether  there  are  not  some  ways  in  which  it  is  being 
restored.  One  of  the  ways  in  which  the  earth's  atmosphere  is 


24  ASTRONOMY 

increased  is  by  the  escape  of  gases  from  the  earth  itself,  particularly 
from  volcanoes  and  hot  springs.  But  perhaps  the  escape  of  gases 
from  the  rocks  as  they  are  dissolved  by  the  action  of  the  water  and 
air  is  equally  important,  for  it  is  found  that  almost  all  the  rocks  of 
the  earth's  surface  contain  in  their  interstices  large  quantities  of  gas, 
which  is  called  occluded  gas. 

There  is  another  way  in  which  the  earth's  atmosphere  is  prob- 
ably to  some  extent  replenished.  It  was  remarked  above  that 
meteors  strike  into  the  earth's  atmosphere  and  are  burned  up  by 
friction  with  it.  When  a  body  is  burned  up  the  material  of  which  it 
is  composed  is  not  utterly  destroyed  but  is  only  changed  in  form. 
For  example,  when  wood  is  burned  the  carbon  in  it  unites  with 
the  oxygen  of  the  air  and  produces  carbon  dioxide,  which  goes 
off  as  a  gas.  Some  of  the  mineral  substances  remain  behind  in  the 
•ashes.  The  vapors  given  off  in  the  process  of  combustion  and 
*the  ashes  left  behind  together  equal  the  total  quantity  of  matter  in  the 
original  wood  plus  the  oxygen  added  to  it  during  the  combustion. 
Therefore,  when  meteors  strike  into  our  atmosphere  and  are  burned, 
the  product  of  the  combustion  is  added  to  the  earth.  If  it  is  solid 
it  slowly  settles  to  the  earth,  and  if  it  is  gaseous  it  becomes  a  part 
of  the  atmosphere.  The  amount  of  atmosphere  added  in  this  manner 
in  a  year  is,  of  course,  small,  but  it  may  be  sufficient  to  make  up 
for  that  which  is  lost. 

It  is  probable,  also,  that  the  region  in  the  neighborhood  of  the 
sun  through  which  the  earth  moves  is  filled  sparsely  with  wandering 
molecules.  They  may  have  been  lost  from  the  earth  and  other 
planets,  or  may  never  yet  have  been  gathered  into  any  large  body. 
If  this  is  true  the  earth  in  its  course  around  the  sun  would  gradually 
gather  them  up  and  in  this  manner  replenish  its  atmosphere. 

It  is  clear  from  what  has  been  said  that  there  are  ways  in  which 
the  earth  loses  its  atmosphere  and  others  in  which  it  tends  to  gain 
one.  There  is  no  astronomical  means  of  determining  whether  the 
loss  is  greater  than  the  gain  or  not.  Probably  the  gain  and  loss  have 
reached  a  state  of  equilibrium'.  If  the  earth  had  a  very  extensive 
atmosphere,  so  that  its  borders  were  farther  from  its  surface  it  would 
lose  it  more  easily  and  consequently  more  rapidly,  while  it  would 
gain  only  a  little  more  than  now.  If  it  ever  had  so  large  an  atmos- 
phere that  it  was  lost  faster  than  it  was  restored,  probably  enough  of 


ASTRONOMY  25 

it  has  been  lost  so  that  it  is  now  in  approximate  equilibrium.  It  is 
somewhat  analogous  to  the  condition  of  a  body  of  water  subject  to 
evaporation.  An  exposed  vessel  of  water  continually  loses  particles 
by  their  leaping  into  the  atmosphere.  It  also  continually  gains  them 
by  those  which  are  in  the  atmosphere  plunging  into  it.  If  the  atmos- 
phere is  initially  very  dry,  then  the  evaporation  is  more  rapid  than 
the  restoration  of  water  from  the  air.  But  as  evaporation  goes  on, 
if  the  atmosphere  above  the  vessel  of  water  is  enclosed,  after  a  time 
a  state  of  equilibrium  is  reached  in  which  the  loss  and  gain  are  exactly 
equal.  Probably  in  a  somewhat  analogous  fashion  the  condition  of 
the  earth's  atmosphere,  respecting  its  loss  into  space  and  the  gain 
from  the  various  possible  sources,  has  reached  a  state  of  equilibrium. 

It  was  stated  above  that  in  order  for  a  molecule  to  escape  from  the 
earth  it  must  leave  its  surface  with  a  velocity  of  approximately  seven 
miles  per  second.  If  the  earth  were  smaller  or  less  dense  it  would  have 
a  smaller  gravitative  power  and  a  molecule  could  escape  by  leaving 
at  a  somewhat  lesser  velocity.  The  moon  is  an  example  of  a  smaller 
world  where  it  is  easier  for  molecules  to  escape.  The  diameter  of  the 
moon  is  about  one-fourth  that  of  the  earth  and  its  mass  about  one- 
eightieth.  If  a  body  leaves  its  surface  with  a  speed  of  1.5  miles 
per  second  it  will  permanently  escape.  It  is  a  significant  fact  in 
this  connection  that  the  moon  has  no  sensible  atmosphere. 

On  the  other  hand,  bodies  which  are  larger  than  the  earth  have 
greater  gravitative  power  and  higher  velocities  of  escape.  In  the 
case  of  the  great  planet  Jupiter,  which  is  nearly  1,000  times  as  big 
as  the  earth  and  has  a  mass  more  than  300  times  as  great,  a  body 
must  leave  its  surface  with  a  velocity  of  over  37  miles  per  second  in 
order  to  escape.  It  is  clear  from  this  that  it  can  control  a  much 
greater  atmosphere  than  the  earth  can;  and  this  theory  is  in  har- 
mony with  the  observed  fact  that  Jupiter  has  a  great  atmosphere. 
In  the  solar  system  the  greatest  body  is  the  sun,  and  the  computa- 
tion shows  that  a  particle  must  leave  its  surface  at  the  rate  of  380 
miles  per  second  in  order  to  permanently  escape.  Obviously,  there 
is  small  chance  for  the  particles  of  an  atmosphere  to  escape  from 
its  control,  and  observation  shows  that  it  has  a  greater  atmosphere 
than  any  other  member  of  our  system. 

Effects  of  Atmosphere  on  Climate.  Aside  from  the  sun  the 
atmosphere  is  the  most  important  influence  affecting  our  climate. 


26  *    ASTRONOMY 

In  the  daytime,  when  the  earth  is  subject  to  the  direct  rays  of  the 
sun,  the  atmosphere  absorbs  a  considerable  part  of  them  and  keeps 
the  temperature  from  rising  to  the  point  it  would  otherwise  reach. 
It  is  difficult  to  determine  what  part  of  the  sun's  radiation  is  absorbed 
in  the  atmosphere,  but  certain  computations  make  it  as  high  as  50 
per  cent.  The  effectiveness  of  the  atmosphere  in  absorbing  the  sun's 
heat  is  noticed  when  one  ascends  a  high  mountain  or  even  lives  on 
an  elevated  plateau.  In  those  exposed  places  the  sun's  radiation 
is  noticeably  more  intense  than  at  the  lower  levels.  Therefore,  one 
effect  of  the  atmosphere  is  to  keep  down  the  temperature  during 
the  middle  of  the  day.  If  the  atmosphere  absorbs  a  certain  amount 
of  the  light  and  heat  coming  from  the  sun,  it  is  not  entirely  lost  to 
the  surface  of  the  earth  because  the  atmosphere  later  radiates  this 
heat  again.  Part  of  it  is  radiated  out  into  space  and  part  of  it  toward 
the  earth.  That  is,  some  of  the  heat  which  comes  from  the  sun  is 
caught  in  the  earth's  atmosphere  in  the  daytime  and  held  there  a 
while  and  delivered  to  the  earth's  surface  by  radiation  at  night. 
In  this  way  the  earth's  atmosphere  makes  the  surface  of  the  earth 
warmer  at  night  than  it  would  otherwise  be. 

Another  effect  of  the  atmosphere  is  that  it  prevents  radiation 
from  the  surface  of  the  earth  at  night.  Though  the  rays  are  not 
visible  the  earth  radiates  heat  out  into  space  as  a  luminous  body 
radiates  light.  The  atmosphere  above  the  surface  of  the  earth  catches 
a  part  of  this  radiated  heat  and  in  turn  radiates  it  again.  A  part  of 
it,  of  course,  comes  back  to  the  earth.  It  is  a  matter  of  common 
observation  that  the  nights  are  very  cool  in  the  high  altitudes,  and 
the  explanation  is  simply  that  the  atmosphere  there  is  so  tenuous 
that  it  does  not  catch  the  heat  which  the  earth  is  radiating.  There- 
fore, considering  the  24  hours,  it  is  seen  that  the  effect  of  the  atmos- 
phere is  to  reduce  the  variations  in  temperature. 

There  is  another  important  way  in  which  the  atmosphere  tends 
to  equalize  temperatures.  The  equatorial  part  of  the  earth  receives 
much  more  light  and  heat  than  the  high  latitudes  and  this  sets  up 
great  currents  in  the  atmosphere.  In  the  northern  hemisphere  the 
atmospheric  currents  are  on  the  whole  from  the  southwest  toward 
the  northeast.  The  point  is  that  the  atmosphere  moves  from  the 
heated  equatorial  regions  toward  the  frozen  regions  of  the  north. 
In  this  manner  enormous  quantities  of  heat  are  carried  from  regions 


ASTRONOMY  27 

where  they  are  not  needed  to  regions  where  otherwise  it  would  be 
very  cold.  The  effects  are  seen  on  the  western  coasts  of  the  large 
land  areas  in  the  northern  hemisphere,  which  in  all  instances  have 
much  warmer  climates  than  corresponding  latitudes  on  the  eastern 
shores.  It  is  clearly  not  because  the  western  shores  receive  more 
heat  from  the  sun,  but  because  they  are  warmed  by  heat  which  fell 
on  the  earth  elsewhere.  Now,  it  is  impossible  for  the  atmosphere 
to  go  northward  in  the  northern  hemisphere  without  an  equal  amount 
going  southward.  The  warm  currents  pass  along  the  surface  of 
the  earth  carrying  the  mild  temperature  into  higher  latitudes, 
and  the  cool  air  from  the  polar  regions  goes  southward  and  reduces 
the  temperature  in  the  equatorial  zone.  In  this  manner  the  tempera- 
ture at  the  surface  of  the  earth  considered  as  a  whole  is  much  more 
uniform  than  it  would  be  except  for  the  atmosphere. 

The  effects  of  the  atmosphere  on  the  climate  depend  to  some 
extent  upon  its  constitution.  This  is  clearly  seen  to  be  so  by  con- 
sidering the  difference  in  temperatures  when  it  is  clear  and  cloudy. 
The  gardener  does  not  fear  a  frost  on  a  cloudy  night  because  he 
knows  the  clouds  keep  in  the  radiations  from  the  earth  and  prevent 
the  temperature  sinking  below  the  freezing  point.  On  the  other 
hand,  when  the  atmosphere  is  clear  and  relatively  free  from  water 
vapor  it  is  more  transparent  to  the  radiations  from  the  earth  and 
the  temperature  falls  more  quickly  and  to  a  lower  point. 

Water  vapor  is  not  the  only  substance  of  the  atmosphere  which 
has  the  property  of  strongly  absorbing  light  and  heat.  Another 
compound  which  is  important  in  this  respect  is  carbon  dioxide. 
Though  the  amount  of  this  substance  is  small  in  the  earth 's  atmos- 
phere it  is  probably  important  in  absorbing  the  solar  radiation.  If 
the  amount  were  considerably  increased  the  mean  temperature  of 
the  earth  would  rise,  and  if  it  were  considerably  decreased  it  would 
fall.  This  is  an  interesting  point  in  connection  with  the  fact  which 
geologists  have  worked  out  for  us,  namely,  that  the  climate  of  the 
earth  has  alternately  been  much  warmer  and  colder  than  it  is  at  the 
present  time.  The  northern  part  of  the  United  States  has  time  after 
time  been  visited  by  great  ice  sheets  which  have  pushed  down  from 
the  North,  and  which  show  that  at  certain  epochs  the  mean  tem- 
perature has  been  much  lower  than  it  is  at  present.  On  the  other 
hand,  in  intervening  epochs  the  temperature  has  been  higher,  for 


28  ASTRONOMY 

in  these  altitudes  and  even  so  far  north  as  Greenland  semi-tropical 
plants  have  flourished.  It  may  be  that  these  oscillations  in  tem- 
perature are  not  due  at  all  to  astronomical  causes  but  only  to  the 
varying  composition  of  the  earth's  atmosphere.  There  are  reasons 
for  believing  that  for  long  periods  the  amount  of  carbon  dioxide  will 
decrease  as  it  becomes  locked  up  in  coal  beds  and  absorbed  by  the 
oceans,  and  that  then  for  long  periods  it  will  increase.  This  change 
may  be  sufficient  to  cause  all  the  climatic  changes  of  which  we  have 
evidence.  It  is  generally  supposed  that  at  the  present  time  the 
amount  of  carbon  dioxide  in  the  atmosphere  is  slowly  increasing  and 
that  the  climate  is  getting  slightly  warmer.  It  should  not  be  under- 
stood, however,  that  the  change  is  rapid  enough  so  that  it  can  be 
observed  for  so  short  a  time  as  a  thousand  years.  Those  changes 
which  are  observed,  or  which  are  supposed  to  have  been  observed, 
are  almost  certainly  of  a  local  and  more  temporary  character. 

It  follows  from  this  discussion  that  if  one  is  to  consider  the 
question  of  the  habitability  of  another  world,  the  question  of  the 
extent  and  nature  of  its  atmosphere  is  a  very  important  one.  In 
the  first  place,  a  definite  constitution  of  the  atmosphere  is  neces- 
sary for  most  of  such  life  processes  as  take  place  upon  the  earth, 
and  in  the  second  place  the  climatic  effects  are  so  important  that 
they  may  be  the  determining  factor. 

Refraction  of  Light  by  the  Atmosphere.  If  light  passes  obliquely 
from  a  rarer  medium  into  a  denser  medium,  its  direction  changes 
slightly  at  the  surface  separating  the  two,  the  amount  of  change 
depending  upon  the  differences  of  densities  and  to  some  extent  upon 
the  constitution  of  the  two  media.  When  the  light  from  a  celestial 
object  enters  our  atmosphere  from  vacant  space  its  direction  is  some- 
what changed.  In  this  case  it  does  not  pass  from  one  medium  into 
another  of  constant  density,  but  as  it  passes  down  through  our  atmos- 
phere it  gets  into  a  medium  whose  density  continuously  increases. 
Consequently,  the  path  of  the  ray  of  light  continually  changes. 

In  Fig.  9,  suppose  the  ray  of  light  comes  from  a  star  S  and 
strikes  the  atmosphere  at  the  point  A.  At  this  point  its  direction 
begins  to  change  and  continually  changes  until  it  reaches  the  sur- 
face of  the  earth  at  0.  An  observer  at  0  sees  the  star  in  the  direc- 
tion from  which  the  light  came  when  it  entered  his  eye;  that  is,  the 
star  seems  to  him  to  be  at  S'.  Since  the  star  is  at  a  distance  which 


ASTRONOMY  29 

is  sensibly  infinite  it  is  actually  in  the  direction  OL.  Of  course,  in 
the  diagram  the  difference  in  direction  is  greatly  exaggerated.  The 
point  to  be  noticed  is  that  the  star  appears  to  be  higher  in  the  sky 
than  it  actually  is. 

This  change  of  direction,  or  atmospheric  refraction,  is  zero  for 
a  star  at  the  zenith,  and  increases  continuously  until  the  horizon  is 
reached.  At  the  horizon  it  is  a  little  over  one-half  a  degree,  the 
exact  amount  depending  upon  several  factors  such  as  the  density  of 
the  air  at  the  time,  i.  e.,  the  barometric  pressure,  the  temperature, 
and  upon  the  amount  of  water  vapor  it  contains. 

One  of  the  consequences  of  the  refraction  of  light  is  that  an 
object  (for  example,  the  sun)  apparently  rises  before  it  actually  is 
above  the  horizon,  and  apparently  does  not  set  until  after  it  is  actually 
below  the  horizon.  That  is,  the  sun  is  apparently  above  the  horizon 
longer  than  it  would  be  except  for  the  refraction.  One  might  infer 


Fig.  9.     The  Light  from  the  Star  S  Is  Bent  as  It  Comes  through  the 
Earth's  Atmosphere  so  That  It  Seems  to  Be  in  the  Direction  S' 

from  this  that  we  get  more  light  and  heat  from  the  sun  than  we  would 
if  it  were  not  for  the  atmosphere.  But  the  absorption  by  the  atmos- 
phere of  the  sun's  light  and  heat  more  than  offsets  this  slight  gain. 

There  is  another  interesting  consequence  of  the  fact  that  the 
refraction  increases  to  the  horizon.  When  the  sun  or  moon  is  on 
the  horizon,  light  from  the  upper  part  is  refracted  less  than  the 
light  from  the  lower  part.  The  lower  part  being  apparently  lifted 
more  than  the  higher  part  makes  it  appear  flattened  in  the  vertical 
direction,  as  illustrated  in  the  case  of  the  sun,  Fig.  10.  This  is  often 
enough  to  be  very  conspicuous,  and  if  it  has  not  been  observed  it 
should  be  looked  for. 

In  making  astronomical  observations  it  is  often  important  to 
locate  the  exact  position  of  the  object.  Now,  it  has  just  been  seen 
that  the  apparent  position  is  different  from  the  exact  position  on 
account  of  refraction.  Consequently,  it  is  necessary  to  make  cor- 


30 


ASTRONOMY 


rections  to  the  direct  observations  for  this  refraction.  An  example 
of  where  this  is  important  is  in  making  observations  at  sea  for  deter- 
mining the  position  of  a  ship.  The  correction  would  be  rather  simple 
if  it  were  not  for  the  fact  that  the  refraction  varies  with  the  state  of 
the  atmosphere.  This  introduces  uncertainties  which  are  important 
when  the  object  under  observation  is  near  the  horizon.  In  the  most 
exact  kind  of  astronomical  work  it  is  important  that  the  observation 
should  be  taken  when  the  object  viewed  is  not  far  from  the  zenith, 
and  this  condition  is  always  secured  if  possible. 


Fig.  10.     The  Refraction  of  Light  Makes  the  Sun  Appear  Flattened 
When  It  Is  Seen  on  the  Horizon 

The,  atmosphere  is  not  only  of  variable  density  from  the  highest 
regions  to  the  surface  of  the  earth,  but  there  are  waves  in  it  which 
cause  the  density  at  a  given  point  continually  to  vary.  This  makes 
constant  changes  in  the  refraction  of  light,  though,  of  course,  of  no 
great  extent.  One  of  the  consequences  of  this  varying  refraction 
is  seen  best  in  observations  of  the  stars.  On  a  clear  night,  especially 
in  the  winter  time,  and  particularly  if  it  is  not  calm,  the  stars  are 
seen  to  twinkle  or  scintillate.  This  twinkling  is  due  entirely  to  the 
fact  that  the  light  from  the  stars  is  passing  through  an  atmosphere 
whose  density  is  constantly  changing  so  that  the  refraction  is 
unsteady.  It  is  easy  to  verify  the  fact  that  the  twinkling  is  greater 
the  nearer  the  star  is  to  the  horizon. 

Relative  Rotation  of  the  Earth.  The  most  casual  observer  of 
the  heavenly  bodies  knows  that  the  stars  rise  in  the  east,  pass  across 
the  sky,  and  set  in  the  west,  just  as  the  sun  and  moon  do.  This 
refers  to  those  which  are  not  near  the  pole  of  the  sky.  Any  observer 


ASTRONOMY 


31 


of  the  stars  can  see  that  those  which  are  near  the  pole  of  the  sky 
go  around  it  in  circles  whose  centers  are  very  close  to  the  pole  star. 
For  example,  if  the  Big  Dipper  is  on  the  east  side  of  the  pole  in  the 
evening  it  will  pass  in  a  circle  around  above  it  during  the  night  and 
be  on  the  west  side  in  the  morning.  If  one  knows  where  it  is  in  the 
evening  he  can  tell  the  time  of  night,  at  least  approximately,  by 
observing  its  position. 


Fig.  11.      Circumpolar  Star  Trails  Photographed  at  the  Yerkes  Observatory 

Fig.  11  shows  the  trails  of  the  stars  in  the  vicinity  of  the  pole 
as  they  were  photographed  during  an  exposure  of  a  little  more 
than  an  hour  with  the  telescope  pointed  to  the  northern  sky  and 
kept  fixed.  The  conspicuous  streak  below  the  center  and  a  little 
to  the  left  is  the  trail  of  the  pole  star  itself,  which  is  thus  shown  to 
be  not  exactly  at  the  pole  of  the  sky.  Most  of  the  stars  whose 
trails  are  shown  are  invisible  to  the  unaided  eye. 


32  ASTRONOMY 

Since  all  heavenly  bodies  rise  in  the  east  (except  those  so  near 
the  pole  they  simply  go  round  it),  travel  across  the  sky,  and  set  in 
the  west  to  reappear  again  in  the  east,  it  follows  that  either  they  go 
around  the  earth  from  east  to  west  or  the  earth  turns  from  west  to 
east.  So  far  as  these  simple  observations  go  it  is  not  possible  to  deter- 
mine which  of  the  two  theories  is  correct.  It  is  incorrect  to  suppose 
that  those  ancients  who  believed  that  the  earth  is  fixed  and  the  sky 
goes  around  it  adopted  any  theory  which  violates  the  common  facts 
of  observation.  This  theory  is  as  much  in  harmony  with  the  apparent 
motions  of  the  heavenly  bodies  as  the  one  we  have,  viz,  that  the 
stars  are  fixed  and  that  the  earth  turns  from  west  to  east.  It  has 
already  been  remarked  that  one  of  the  characteristics  of  science  is 
that  it  gives  reasons  for  its  conclusions.  Therefore,  it  will  be  necessary 
to  take  up  and  explain  the  reasons  we  have  for  believing  that  the 
earth  moves  and  that  the  sky  is  fixed.  Before  taking  up  the  question 
of  the  motions  of  the  earth  in  particular,  we  shall  consider  the  laws 
of  motion  of  bodies  in  general. 

Laws  of  Motion.  The  laws  of  nature  are  in  an  important  respect 
different  from  civil  laws,  and  it  is  to  some  extent  unfortunate  that 
the  same  term  is  used.  A  civil  law  prescribes  a  mode  of  conduct 
and  penalties  if  it  is  violated.  A  civil  law  can  be  broken  at  will  if 
one  is  willing  to  accept  the  penalty,  or  at  least  the  chance  of  it.  A 
natural  law,  or  a  law  of  nature,  on  the  other  hand,  does  not  pre- 
scribe anything,  but  is  a  statement  of  the  way  all  phenomena  of 
a  certain  class  proceed.  If  it  is  a  true  law  of  nature  it  describes 
the  way  phenomena  invariably  proceed  and  there  are  no  exceptions 
to  it. 

The  laws  of  motion  are  statements  of  the  way  bodies  actually 
move.  They  were  first  given  in  their  completeness  by  Newton  in  the 
Principia  in  1686,  although  they  were  to  some  extent  understood  by 
his  predecessor  Galileo.  They  were  called  by  Newton  axioms, 
although  they  can  hardly  be  said  to  be  axioms  in  the  ordinary  sense 
of  the  term,  since  for  thousands  of  years  men  believed  motions 
were  different  from  what  they  are  as  expressed  by  these  laws.  The 
laws,  essentially  as  Newton  gave  them,  are: 

LAW  I.  Every  body  continues  in  its  state  of  rest  or  of  uniform 
motion  in  a  straight  line  unless  it  is  compelled  to  change  that  state  by 
exterior  forces  acting  upon  it. 


ASTRONOMY  33 

LAW  II.  The  rate  of  change  of  motion  is  proportional  to  the  force 
impressed  and  the  change  takes  place  in  the  direction  of  the  straight 
line  in  which  the  force  acts. 

LAW  III.  To  every  action  there  is  an  equal  and  opposite  reaction; 
or,  mutual  actions  of  bodies  are  always  equal  and  oppositely  directed. 

The  importance  of  these  laws  can  be  understood  from  the  fact 
that  every  astronomical  phenomenon  involving  the  motion  of  matter, 
and  everything  upon  the  earth  involving  the  motion  of  matter,  is 
interpreted  by  using  them  as  a  basis.  A  little  reflection  will  show 
that  there  are  few  things,  indeed,  which  are  not  associated  with  the 
motion  of  matter.  Even  the  process  of  thinking  is  probably  asso- 
ciated with  the  motion  of  matter  in  the  changing  structure  of  the 
brain.  Because  of  the  wide  application  of  these  laws  it  is  necessary 
to  give  them  careful  attention. 

The  first  law  states  the  important  fact  that  if  a  body  is  at  rest 
it  will  never  begin  to  move  unless  some  force  acts  upon  it,  and  if 
it  is  in  motion  it  will  forever  move  at  uniform  speed  in  a  straight 
line  unless  some  exterior  force  acts  upon  it.  This  in  two  respects  is 
opposite  to  the  views  held  generally  before  the  time  of  Newton.  In 
the  first  place,  it  was  supposed  that  bodies  would  descend  without 
forces  acting  upon  them.  In  the  second  place,  it  was  supposed  that 
if  a  body  were  in  motion  it  would  stop  unless  some  force  were  con- 
tinually applied  to  keep  it  going.  These  errors  prevented  the  prede- 
cessors of  Newton  getting  any  satisfactory  explanation  of  the  motions 
of  the  heavenly  bodies. 

The  second  law  means  by  the  "rate  of  change  of  motion"  the 
product  of  the  mass  and  the  rate  of  change  of  velocity.  It  might 
be  made  to  read,  the  rate  of  change  of  velocity  is  proportional  to  the 
force  impressed  and  inversely  proportional  to  the  mass  moved,  and 
the  change  takes  place  in  the  direction  of  the  straight  line  in  which 
the  force  acts.  The  first  two  laws  consider  a  single  body  subject  to 
exterior  forces. 

The  third  law  expresses  the  way  in  which  two  bodies  act  on 
each  other.  It  means  essentially  that  no  body  can  change  the  state 
of  the  motion  of  another  body  without  having  its  own  motion  cor- 
respondingly changed,  and  this  is  equally  true  whether  the  bodies 
are  in  actual  contact  or  connected  by  some  invisible  bond  of  force 
such  as  gravitation.  The  difficulties  in  getting  a  clear  mental  picture 


34  ASTRONOMY 

of  this  law  come  largely  from  the  fact  that  it  is  not  possible  to  get 
two  bodies  subject  only  to  their  mutual  interactions.  If  a  man  and 
a  small  boy  pull  in  opposite  directions  on  a  rope,  the  man  pulls  the 
boy,  and  it  seems  that  the  law  is  violated.  The  reason  of  the  apparent 
violation  of  it  is  due  to  the  fact  that  there  are  other  forces  in  operation, 
particularly  the  friction  of  the  feet  of  the  man  and  the  boy  with  the 
ground.  If  they  were  both  in  small  boats  on  the  water,  then  each 
would  move  with  a  speed  inversely  proportional  to  his  mass.  It 
follows  from  this  fact,  which  we  shall  suppose  is  verified  in  experi- 
ment, and  the  second  law  of  motion,  that  the  forces  are  equal  and 
opposite.  The  more  nearly  the  exterior  forces  are  eliminated  the 
more  nearly  the  law  is  verified.  It  is  to  be  understood  that  the  laws 
of  motion  can  be  verified  with  a  high  degree  of  precision  in  the  labora- 
tory. They  have  been  tested  in  this  manner  thousands  of  times  and 
no  deviations  from  them  have  been  observed  that  can  not  be  explained 
by  extraneous  forces  which  it  was  not  possible  to  eliminate.  They 
have  also  been  verified  indirectly  in  thousands  of  ways,  and  some  of 
these  verifications,  particularly  in  astronomy,  are  more  exact  than 
any  of  a  direct  character.  Just  as  railway  trains  obey  the  laws  of 
motion  and  in  consequence  would  jump  the  track  on  curves  if  the 
outside  rails  were  not  elevated,  so  also  the  heavenly  bodies  in 
their  motions  obey  the  laws.  But  in  the  case  of  heavenly  bodies  the 
disturbing  factors  are  almost  entirely  absent,  and  the  operation  of 
the  laws  is  observed  under  almost  ideal  conditions. 

Rotation  of  the  Earth  Proved  by  Eastward  Deviation  of  Falling 
Bodies.  If  the  earth  rotates,  then  the  farther  a  body  is  from  its  axis 
the  faster  it  goes.  The  circumference  of  the  earth  at  the  equator  is 
about  25,000  miles,  so  that  a  body  on  the  surface  of  the  earth  at  the 
equator  moves  eastward  if  the  earth  rotates  at  the  rate  of  about 
1,000  miles  an  hour.  r 

In  Fig.  12,  suppose  that  C  is  a  point  on  the  axis  of  the  earth 
and  that  CP  is  a  line  perpendicular  to  it.  Suppose  0  is  the  top  of  a 
high  tower  whose  base  is  at  P  (of  course,  the  height  of  the  tower  is 
greatly  exaggerated  in  the  figure),  and  suppose  the  earth  rotates  in 
the  direction  PPr  and  that  the  line  CP  moves  to  CP'  in  one  unit  of 
time.  Therefore,  a  mass  at  the  bottom  of  the  tower  has  the  velocity 
PP'.  Now,  consider  a  body  at  the  top  of  the  tower  0  whose  velocity 
is  00' .  When  the  body  is  dropped  its  motion  will  be  the  resultant 


ASTRONOMY  35 

of  its  motion  toward  0'  and  of  the  attraction  of  the  earth  for  it  toward 
C.  This  attraction  is  at  right  angles  to  the  line  00'  and  will,  there- 
fore, not  diminish  the  velocity  in  this  direction.  Hence,  in  the  unit  of 
time  the  body  will  move  precisely  as  far  eastward  as  though  it  were 
not  falling.  Since  the  earth's  attraction  acts  continuously  it  will  fall 
faster  and  faster  until  it  strikes  the  surface  of  the  earth.  The  curve 
described  by  the  body  will  be  OQ,  Q  being  the  point  where  it  strikes 
the  earth.  This  point  will  be  east  of  the  foot  of  the  tower  P'  at 
the  time  it  strikes  the  surface  because  the  distance  00'  is  greater 
than  PP'.  Therefore,  the  falling  body  will  have  an  eastward  devia- 
tion. On  the  other  hand,  if  the  earth  were  not  rotating  it  would 
strike  at  the  foot  of  the  tower. 

From  this  discussion  we  see  how  the 
body  will  fall  if  the  earth  rotates  and  how 
it  will  fall  if  it  does  not.  The  experiment 
will  decide  the  matter.  The  problem  is 
one  of  some  practical  difficulty  because 
very  slight  air  currents  will  cause  enough 
change  in  motion  to  mask  the  small  east- 
ward deviation,  which  in  our  latitude 
amounts  to  only  about  an  inch  in  a  fall 
of  five  hundred  feet.  The  most  successful 
experiments  have  been  carried  out  in  mine  ,,. 

Fig.  12.     The  Eastward  Devia- 

shaf ts  where  large  falls  can  be  secured  and     ti  tSe^ftation  3°the8  Ewth68 
where  by  covering  them  the  air  currents 

can  be  destroyed.  The  experiments  have  actually  shown  the  east- 
ward deviation,  and  therefore  have  proved  the  eastward  rotation  of 
the  earth. 

Rotation  of  the  Earth  Proved  by  Its  Shape.  It  follows  from  the 
laws  of  motion  stated  above,  and  the  law  of  gravitation,  that  if  the 
earth  does  not  rotate  it  will  be  exactly  spherical  except  for  slight 
irregularities  due  to  its  lack  of  homogeneity.  It  also  follows  from 
the  laws  of  motion  that  if  it  is  rotating  it  will  be  bulged  at  the  equa- 
tor and  flattened  at  the  poles.  The  first  law  of  motion  asserts 
that  a  body  subject  to  no  forces  will  move  in  a  straight  line. 
Now,  the  particles  at  the  earth's  surface,  especially  at  the  equator, 
tend  to  move  in  a  straight  line  in  harmony  with  this  law,  and  are 
held  to  the  earth  only  by  its  attraction.  This  tendency  to  move 


36 


ASTRONOMY 


out  in  straight  lines  produces  the  equatorial  bulge.  If  the  earth 
moved  seventeen  times  as  fast  as  it  does  now  and  were  of  the  same 
size  and  shape,  a  loose  particle  on  its  surface  at  the  equator  would  fly 
away  into  space. 

It  is  seen  that  if  the  earth  did  not  rotate  it  would  be  round,  and 
that  if  it  did  rotate  it  would  be  oblate.  The  observations  again  must 
settle  the  question  as  to  which  is  true.  As  was  explained  above, 
measurements  of  arcs  on  the  surface  of  the  earth  have  shown  con- 
clusively that  the  earth  is  bulged  at  the  equator  and  flattened  at 
the  poles.  Therefore,  we  are  forced  to  the  conclusion  that  the 
earth  rotates.  This  method  of  proving  its  rotation  gives  us  the 
position  of  its  axis  but  does  not  determine  for  us  which  way  it 

moves. 

Rotation  of  the  Earth  Proved  by  Fou= 
cault's  Pendulum  Experiment.  It  follows 
from  the  laws  of  motion  that  a  pendulum 
set  swinging  tends  to  move  continually  in 
the  same  plane.  Let  us  imagine  a  pen- 
dulum suspended  from  A,  Fig.  13,  over 
the  exact  pole  of  the  earth,  and  suppose 
that  it  is  started  swinging  in  the  plane  of 
the  meridian  m.  If  it  is  subject  to  no 
other  force  than  the  attraction  of  the  earth, 
which  is  directed  toward  the  earth's  center, 
it  will  continually  swing  in  this  plane.  Let  us  suppose  that  the  earth 
is  rotating  toward  the  east,  the  direction  being  indicated  by  the  arrow 
on  the  equator  in  Fig.  13.  The  meridian  m  will  turn  in  the  direction 
of  the  arrow  while  the  pendulum  stays  fixed.  If  an  observer  were  on 
the  earth  at  the  pole  the  earth  would,  of  course,  seem  to  him  fixed 
as  it  does  to  us  where  we  live,  but  the  pendulum  would  seem  to  him 
to  be  turning  in  the  westward  direction.  If  he  should  watch  it  for 
24  hours  he  would  find  that  it  made  a  complete  apparent  revolution 
in  that  time. 

If  the  pendulum  were  suspended  at  the  equator  instead  of  at 
the  pole  there  would  be  no  more  tendency  for  it  to  rotate  in  one 
direction  than  the  other,  and,  as  can  be  easily  seen,  it  would  not 
change  the  apparent  plane  of  its  vibration.  Therefore,  an  observer 
there  would  notice  no  rotation  of  the  pendulum. 


Fig.  13.     Proof  of  Earth's  Rota- 
tion by  Foucault  Pendulum 


ASTRONOMY  37 

Now,  consider  a  point  between  the  pole  and  the  equator.  At 
the  pole  the  plane  of  the  pendulum's  motion  rotates  in  24  hours  and 
at  the  equator  it  does  not  rotate  at  all.  In  the  intermediate  latitude 
it  rotates  but  the  period  is  longer  than  24  hours,  its  length  depending 
upon  the  latitude.  In  our  latitude  the  period  of  apparent  rotation  is 
about  36  hours. 

It  follows  from  this  discussion  that  if  a  pendulum  is  set  swing- 
ing in  our  latitude,  the  plane  of  it  apparently  slowly  deviates  to  the 
west  if  the  earth  rotates  to  the  east.  On  the  other  hand,  if  the  earth 
is  fixed,  it  will  continually  swing  in  the  same  plane.  The  experiment 
must  be  made  in  order  to  prove  which  theory  is  correct.  This  very 
ingenious  and  convincing  method  of  proving  the  rotation  of  the 
earth  was  devised  and  carried  out  by  Foucault,  in  Paris,  in  1851. 
He  suspended  a  heavy  iron  ball  by  a  steel  wire  about  200  feet  in 
length.  It  was  pulled  to  one  side  of  its  lowest  point  and  fastened  by 
a  thread  and  left  until  it  came  perfectly  to  rest.  Then  the  thread 
was  burned  so  as  not  to  give  it  any  sidewise  disturbance,  and  it 
began  to  swing.  Underneath  it  the  floor  was  marked  so  that  the 
direction  of  its  swing  could  be  seen  easily.  It  was  observed  then  that 
hour  after  hour  it  apparently  deviated  to  the  west,  which  meant, 
of  course,  that  the  earth  was  turning  to  the  east  undef~TE  This 
experiment  can  be  easily  performed  in  space  where  "a^haft  of  con- 
siderable length,  free  from  disturbances,  can  be  secured.  In  carry- 
ing out  the  experiment  it  is  necessary  to  be  careful  to  start  the 
pendulum  swinging  in  an  exact  plane,  for  if  it  has  a  slight  elliptical 
motion  it  will  perform  a  rotation  independent  of  that  produced  by 
the  actual  motion  of  the  earth.  Since  this  experiment  has  been 
many  times  performed  and  has  always  shown  a  westward  apparent 
deviation  in  harmony  with  the  theory,  we  must  conclude  also  from 
this  line  of  evidence  that  the  earth  rotates  eastward. 

Analogy  with  Other  Heavenly  Bodies.  It  is  found  from  observa- 
tions which  do  not  depend  upon  the  theory  that  the  earth  rotates  or 
does  not  rotate,  that  many  of  the  other  heavenly  bodies  are  com- 
parable to  the  earth  in  size.  The  moon  and  some  of  the  planets 
are  smaller;  Venus  is  about  the  size  of  the  earth;  Jupiter  is  about 
one  thousand  times  greater ;  and  the  sun  about  a  million  times  greater. 
Our  modern  powerful  telescopes  show  markings  on  many  of  these 
objects  of  such  a  character  that  it  can  be  determined  whether  they 


38  ASTRONOMY 

rotate  or  not.  It  is  found  that  all  of  them  on  which  markings  can 
be  observed  turn  on  their  axes,  and  what  is  a  remarkable  fact,  in  the 
same  direction.  The  periods  of  their  rotation  vary  considerably. 
For  example,  that  of  the  moon  is  27i  days,  Jupiter  about  10  hours, 
and  the  sun  about  25  days.  But  the  essential  point  of  interest  here 
is  that  these  other  bodies,  which  are  in  most  essential  respects  similar 
to  the  earth,  some  being  smaller  and  some  larger,  all  rotate.  It  is 
not  reasonable,  therefore,  to  suppose  that  the  earth  is  the  one  excep- 
tion. Hence,  we  should  conclude  from  this  alone  that  the  earth 
does  rotate,  though  this  proof  is  by  no  means  so  conclusive  as  the 
proofs  given  above. 

Uniformity  of  the  Earth's  Rotation.  It  follows  from  the  laws 
of  motion,  and  in  particular  from  the  first  law,  that  if  the  earth 
were  subject  to  no  external  forces  and  were  fixed  in  size  and  shape, 
it  would  rotate  on  its  axis  with  absolute  uniformity.  One  might 
suppose  the  matter  could  be  tested  by  comparing  it  with  clocks. 
But  as  a  matter  of  fact  all  the  clocks  which  have  been  made,  and 
which  probably  can  be  made,  run  with  so  much  greater  irregularity 
than  the  earth  rotates  that  no  test  of  this  character  can  succeed. 
In  fact,  the  rotation  of  the  earth  is  used  to  check  the  running  of 
clocks  and  to  regulate  them  when  they  depart  from  perfect  adjust- 
ment. 

One  might  test  the  rotation  of  the  earth  by  comparing  it  with 
some  other  celestial  phenomenon  which  is  known  to  proceed  uni- 
formly. There  are,  however,  no  such  phenomena.  Probably  the 
earth  is  as  good  a  measurer  of  time  as  anything  which  can  be  observed. 
The  best  we  can  do  is  to  discuss  those  forces  and  changes  which  have 
a  tendency  to  change  its  rate  of  rotation. 

The  earth  is  rotating  in  the  luminous  ether  and  a  considerable 
quantity  of  meteoric  matter.  The  latter,  if  not  the  former,  has  a 
tendency  to  retard  its  rotation  and  consequently  to  make  the  day 
a  little  longer.  But  this  resistance  is  exceedingly  small  and  certainly 
does  not  lengthen  the  day  by  a  second  in  1,000,000  years. 

The  moon  and  sun  generate  tides  in  the  earth  which  on  the 
whole  move  around  it  in  a  westerly  direction,  because  these  bodies 
in  their  apparent  motions  move  to  the  westward.  The  tides,  there- 
fore, on  the  whole,  beat  in  upon  the  eastern  shores  and  act  as  a  break 
on  the  rotation  of  the  earth.  While  there  can  be  no  doubt  whatever 


ASTRONOMY  39 

that  the  tides  slow  up  the  rotation  of  the  earth  to  some  extent,  the 
amount  of  the  retardation  is  probably  so  small  as  to  be  of  no  impor- 
tance whatever.  It  is  not  possible  to  measure  it  with  any  degree  of 
exactness,  but  it  is  not  likely  that  the  earth's  day  increases  in  length 
from  this  cause  one  second  in  500,000  years. 

The  interior  of  the  earth  is  hot  and  it  is  gradually  losing  heat 
by  conduction  to  the  surface  and  radiation  into  space.  As  it  loses 
heat  it  probably  shrinks  a  little.  If  a  rotating  body  shrinks  it  rotates 
faster.  The  principle  upon  which  this  statement  is  based,  which  is 
a  conclusion  drawn  from  the  laws  of  motion,  is  that  in  a  rotating 
body  subject  to  no  exterior  forces  the  whole  quantity  of  rotation  is 
a  constant.  By  quantity  of  rotation  is  meant  the  mass  multiplied 
by  the  velocity  multiplied  by  the  distance  from  the  axis  of  rotation. 
Therefore,  if  a  body  shrinks  so  that  the  distance  of  each  mass  in  it 
from  the  axis  of  rotation  becomes  less,  the  velocity  must  be  increased 
in  order  to  restore  the  equality.  Theoretically  this  effect  would  lead 
to  a  shortening  of  the  day.  But  the  earth's  contraction,  because  of  heat 
losses,  is  so  slow  that  probably  the  length  of  the  day  is  not  dimin- 
ished in  this  way  by  so  much  as  one  second  in  twenty  million  years. 

There  are  certain  other  causes  besides  its  shrinking  which  change 
the  distance  of  matter  from  its  axis  of  rotation.  For  example,  if  a 
river  runs  from  high  latitudes  to  low  latitudes,  as  the  Mississippi, 
and  if  it  carries  sediment  in  its  waters  and  deposits  it  in  low  latitudes, 
by  this  process  matter  is  taken  from  a  certain  distance  from  the 
earth's  axis  and  left  at  a  greater  distance  from  it.  So  far  as  this  factor 
is  concerned,  the  earth  is  to  some  extent  retarded  in  its  rotation. 
Not  all  rivers,  however,  run  toward  the  equator  and  those  flowing 
in  the  opposite  direction  offset  this.  The  evaporation  of  water  in 
equatorial  regions  and  its  deposit  as  snow  in  the  higher  latitudes  is 
a  factor  working  in  the  other  direction  and  there  are,  also,  many  rela- 
tively minute  surface  changes,  some  acting  one  way  and  some  another. 

Some  of  the  causes  which  have  been  enumerated  above  tend 
to  increase  the  rate  of  rotation  and  others  to  decrease  it.  It  is  not 
possible  to  determine  at  the  present  time  whether,  on  the  whole, 
the  day  is  becoming  longer  or  shorter.  The  only  thing  certain  about 
it  is  that  the  rate  of  change  is  exceedingly  slow  and  will  not  produce 
sensible  results  before  millions  of  years  have  elapsed.  This  is  a 
question  of  some  practical  interest  because  if  the  day  should  become 


40 


ASTRONOMY 


very  much  longer,  say  forty  hours  in  length,  the  temperature  in  our 
latitudes  would  fall  so  low  nearly  every  night  in  the  year  that  there 
would  be  killing  frosts.  Again,  in  the  correspondingly  longer  day  the 
temperature  would  rise  higher  than  under  present  conditions. 

Variation  of  Latitude.    In  the  preceding  paragraph  the  discussion 
referred  to  the  possible   change   of  the   rate   of   rotation   of  the 


Fig.  14.     The  Path  of  the  Earth's  Pole  from  1900  to  1908 

earth  on  its  axis.  The  question  before  us  now  is  whether 
the  earth  continually  rotates  around  some  fixed  axis.  It  has 
sometimes  been  supposed  by  those  not  familiar  with  the  dynamics 
of  the  question  that  the  former  warm  temperatures  in  the  high 
latitudes  and  the  cold  temperatures  in  the  low  latitudes  might 
be  accounted  for  by  a  change  in  the  position  of  the  axis  of  the 
earth.  It  is  not  dynamically  impossible  that  the  axis  of  rota- 


ASTRONOMY  41 

tion  should  change,  but  if  it  does  change  it  would  be  in  the  nature 
of  an  oscillation  around  some  mean  position.  That  is,  the  earth 
might  have  a  sort  of  wabbling  motion,  just  as  a  top  has  when  it  is 
not  running  steadily.  Observations  made  for  the  purpose  of  detect- 
ing wabbling  did  not  succeed  until  about  thirty  years  ago.  The 
reason  of  the  failure  was  that  the  amount  of  deviation  was  exceedingly 
minute.  This  wabbling  is  spoken  of  as  the  variation  of  latitude, 
or  the  variation  of  the  position  of  the  pole,  the  movements  covering 
a  territory  about  60  feet  in  diameter,  Fig.  14. 

If  a  top  is  running  so  steadily  that  it  "sleeps"  it  will  run  per- 
manently in  that  condition  unless  disturbed  by  some  exterior  force. 
As  a  matter  of  fact,  there  are  many  exterior  forces  always  operating 
on  the  top.  Similarly,  if  the  earth  were  rotating  around  the  axis 
of  its  figure  it  would  forever  run  that  way  unless  it  were  disturbed 
by  external  forces,  or  by  some  redistribution  of  its  own  mass.  As 
has  been  stated,  there  is  a  slight  wabbling  and  the  question  at  once 
arises  as  to  what  are  the  causes  which  have  produced  it.  At  the 
present  time  they  are  not  known.  There  are  many  things  which 
have  some  influence  upon  it,  such  as  the  varying  wind  and  ocean 
currents  during  the  year,  and  the  deposition  of  snow  in  the  high 
latitudes.  Also  the  attractions  of  the  moon  and  sun  on  the  equa- 
torial bulge  may  have  some  effect. 

The  nature  of  the  causes  is  indicated  to  some  extent  by  the  char- 
acter of  the  wabbling.  If  the  earth  were  not  disturbed  it  would 
wabble  in  a  perfectly  definite  fashion,  depending  upon  its  mass,  size, 
shape,  and  rate  of  rotation,  and  would  forever  continue  to  wabble 
in  this  fashion  if  it  were  perfectly  rigid.  The  period  of  this  wabbling 
is  also  a  perfectly  definite  quantity.  The  observations  have  shown 
that  the  wabbling  is  of  a  complicated  character,  being  really  the 
result  of  two  separate  motions.  One  has  a  period  of  one  year,  and 
the  other  of  about  430  days.  The  yearly  period  is  not  the  natural 
one  for  the  earth's  wabbling  and  consequently  this  irregularity 
must  be  produced  by  a  continually  acting  force  whose  period  of 
change  is  one  year.  The  other  irregularity  is  that  one  which  the  earth 
would  have  if  it  were  left  entirely  free  from  external  disturbances. 
Now,  430  days  is  not  the  period  the  earth's  wabbling  would  have  if 
it  were  absolutely  rigid.  If  it  were  a  perfect  solid,  yielding  to  no 
forces  however  great,  its  period  of  wabbling  would  be  about  305 


42 


ASTRONOMY 


days.  But  if  its  rigidity  were  only  that  of  steel,  which  must  be  con- 
sidered highly  elastic  in  treating  of  so  great  a  mass  as  the  earth, 
then  its  period  of  wabbling  would  be  about  440  days,  which  is  near 
that  actually  observed.  It  follows  from  this  that  the  rigidity  of  the 
earth  is  between  that  of  the  perfectly  unyielding  solid  and  that  of 
steel,  and  that  it  is  near  that  of  steel.  Therefore,  we  have  here  a 
new  proof  that  the  rigidity  of  the  earth,  when  considered  through 
and  through,  is  about  that  of  steel. 

Apparent  Motion  of  the  Sun  with  Respect  to  the  Stars.  The 
rising  and  the  setting  of  the  sun  are  such  conspicuous  phenomena 
that  the  most  careless  observer  understands  them  well.  But  it  is  not 

so  well  known  that  the  sun  has 
a  motion  among  the  stars.  It 
moves  eastward  about  as  the 
moon  does,  only  less  rapidly. 
Nearly  everyone  has  noticed  the 
fact  that  the  moon  moves  day  by 
day  eastward  among  the  stars. 
The  reason  the  phenomenon  is 
not  noticed  in  the  case  of  the  sun 
is  that  the  stars  can  not  be  seen 
in  its  immediate  vicinity.  But 
indirectly,  the  fact  can  be  easily 
established  and  was  well  known 
in  remote  antiquity. 
Suppose  a  certain  group  of  stars  is  on  the  meridian  at  midnight 
when  the  sun  is  exactly  opposite.  That  is,  if  one  starts  at  the  sun  and 
goes  eastward  along  the  sky  until  he  gets  to  the  stars  he  finds  them 
at  a  distance  of  180  degrees.  Suppose  that  after  a  month  the  same 
group  of  stars  is  found  30  degrees  west  of  the  meridian  at  midnight. 
In  this  case,  starting  from  the  sun  and  going  eastward  along  the  sky 
to  the  stars,  he  has  to  go  a  distance  of  180°— 30°,  or  150°.  Since  it  is 
now  150  degrees  from  the  sun  to  these  stars,  while  a  month  before 
it  was  180  degrees,  it  means  that  the  sun  has  gone  eastward  among 
them  30  degrees.  Just  such  facts  as  these  are  actually  established 
by  the  observations.  Every  month  in  the  year  the  sun  goes  east- 
ward among  the  stars  30  degree?.  It  can  be  indirectly  established, 
as  has  just  been  explained,  and  more  directly  by  the  use  of  large  tele- 


rig.  15.     The  Sun  Would  Have  an  Apparent 

Eastward  Motion  If  the  Earth  Were  Fixed 

with  the  Sun  Moving  Around  It 


ASTRONOMY  43 

scopes  which  will  show  the  brightest  stars  fairly  close  to  the  sun.  Hence 
the  question  of  the  explanation  of  this  phenomenon  arises. 

In  Fig.  15,  suppose  E  represents  the  earth  which  is  fixed  except 
for  its  rotation  which  was  proved  above.  Suppose  the  sun  moves 
around  the  earth  in  the  curve  SiS2S3S^  When  it  is  at  the  point  Si  it 
is  opposite  the  stars  at  s3  and  in  the  direction  of  the  stars  at  s^ 
The  stars  at  s3  are  visible  on  the  meridian  at  midnight  and  those  at 
Si  can  be  seen  only  with  a  telescope.  Counting  in  the  direction  of 
motion  from  5j  to  s3  the  distance  is  found  to  be  180  degrees.  In  a 
month  suppose  the  sun  is  at  S2.  Then  the  stars  at  #3  are  30  degrees 
west  of  the  meridian  at  midnight  and  those  at  s2  are  in  the  direction 
of  the  sun  and  can  be  seen  only 
with  a  telescope.  Now,  the  dis- 
tance from  $2  forward  in  the  di- 
rection of  the  sun's  motion  to  s3 
is  150  degrees.  As  the  sun  pro- 
ceeds around  the  earth  it  is  suc- 
cessively seen  in  all  directions 
from  the  earth.  This  is  in  perfect 
harmony  with  the  facts  of  obser- 
vation as  recorded  above.  Con- 
sequently, it  is  easy  to  see  why 
the  ancients  were  satisfied  with 

Fig.  16.     The  Motion  of  the  Earth  around 

the  theory  that  the  earth  is  the          the  ^as^a^ramotgThl'starg0  M°ve 
center  of  the  universe,  since  they 

had  only  those  observations  which  we  have  mentioned,  and  which 
have  just  been  shown  to  be  in  harmony  with  this  theory. 

Now,  suppose  S,  in  Fig.  16,  represents  the  sun,  and  that  the 
earth  moves  around  it  in  the  curve  EiE2E3E^.  When  the  earth  is 
at  El  the  sun  is  in  the  direction  of  the  stars  at  s^.  Suppose  the  earth 
moves  forward  in  its  orbit  to  E2  in  one  month.  The  sun  then  appears 
to  be  among  the  stars  at  s2,  and  as  the  earth  moves  forward  in  its 
orbit  the  sun  apparently  moves  forward  among  the  stars  and  com- 
pletes a  circuit  of  the  heavens,  while  the  earth  goes  around  the  sun. 
It  is  seen  that  the  apparent  motion  of  the  sun  in  this  case  is  exactly 
the  same  as  that  when  the  earth  was  supposed  to  be  fixed  at  the 
center  and  the  sun  to  go  around  it.  This  theory  is  therefore  in  as 
perfect  harmony  with  the  ordinary  observations  of  the  apparent 


44  ASTRONOMY 

motion  of  the  sun  as  the  preceding,  and  the  ancients  might  have 
adopted  it  as  well  as  the  other.  As  a  matter  of  fact,  the  heliocentric 
theory,  as  this  is  called,  was  advanced  by  the  ancient  Greeks.  How- 
ever, it  is  clear  from  this  discussion  that  the  facts  furnished  by  obser- 
vations of  the  apparent  motion  of  the  sun  are  not  sufficient  to  enable 
us  to  decide  which  of  the  two  theories  is  the  correct  one. 

The  proofs  that  the  sun  is  the  center  and  that  the  earth  revolves 
around  it  will  be  gone  into  with  some  care.  This  was  a  subject  of 
bitter  discussion  for  many  centuries,  but  the  matter  was  settled 
three  hundred  years  ago  in  the  days  of  Copernicus  and  Galileo,  and 
has  been  open  to  no  question  whatever  since  the  time  of  Newton. 
The  first  modern  astronomer  to  develop  definitely  the  heliocentric 
theory  and  to  attempt  to  work  out  the  motions  of  the  heavenly 
bodies  and  in  particular  the  sun  upon  it,  was  Copernicus  (1473-1543). 
It  is  to  be  understood  that  not  only  is  the  motion  of  the  sun  to  be 
explained,  but  the  motion  of  the  planets  with  respect  to  it,  and  this 
complicates  the  question  greatly.  Copernicus  succeeded  in  showing 
that  the  heliocentric  theory  is  in  harmony  with  all  the  observed 
motions  of  his  time,  and  he  drew  the  conclusion  that  this  is  the  cor- 
rect theory  since  it  is  more  reasonable  than  that  the  relatively  small 
earth  is  the  center  for  the  motions  of  all  the  great  bodies,  especially 
for  that  of  the  sun.  He  did  not  have  what  we  would  now  regard  as 
a  strict  proof  of  the  correctness  of  this  theory. 

Revolution  of  the  Earth  Proved  by  the  Parallax  of  the  Stars. 
Let  us  suppose  that  the  stars  are  fixed  objects  in  the  heavens. 
Then,  if  the  earth  is  the  center  and  the  sun  goes  around  it,  they 
will  always  appear  in  absolutely  the  same  directions.  On  the  other 
hand,  if  the  sun  is  the  center  and  the  earth  revolves  around  it,  they 
will  appear  in  slightly  different  directions  at  different  times  of 
the  year. 

In  Fig.  17  let  S  represent  the  sun  and  AB  the  orbit  of  the  earth. 
Suppose  s  is  one  of  the  fixed  stars.  When  the  earth  is  at  A  this  star 
will  be  seen  in  the  direction  As; 'six  months  later  when  the  earth  is 
at  B  it  will  be  seen  in  the  direction  Bs,  Every  star  will  be  slightly 
displaced  in  this  fashion  because  of  the  earth's  motion  around  the 
sun.  This  difference  in  direction  of  a  star,  as  seen  at  two  different 
times  of  the  year,  is  called  its  parallax.  Consequently,  in  order  to 
determine  whether  the  earth  is  fixed  or  moves  around  the  sun,  it  is 


ASTRONOMY  45 

only  necessary  to  observe  whether  the  directions  of  the  stars  are 
absolutely  fixed  or  not. 

It  is  clear  from  the  figure  that  the  farther  the  star  is  away  the 
smaller  will  be  its  change  in  direction  as  seen  from  the  two  points  A 
and  B.  It  is  analogous  to  the  fact  that  if  one  looks  at  an  object  near 
his  face,  first  with  one  eye  and  then  with  the  other,  he  will  see  it  in 
somewhat  different  directions.  If  he  looks  at  it  with  both  eyes  it  will 
be  necessary  for  him  to  turn  them  in  slightly.  As  a  matter  of  fact, 
one  of  the  best  ways  he  has  of  judging  distance  is  by  the  amount  he 
has  to  turn  the  eyes  in  to  see  the  object.  If  he  looks  at  a  distant  object 
his  eyes  are  sensibly  parallel.  In  Fig.  17,  the  points  A  and  B  corre- 
spond to  the  positions  of  the  two  eyes  of  the  observer,  and  the  star 
to  the  object  observed. 


Fig.  17.     The  Difference  in  Direction  of  the  Star  S  as  Seen  from  the  Earth  at 
Two  Different  Times  of  the  Year  Proves  the  Revolution  of  the  Earth 

The  fact  that  the  stars  should  have  parallaxes  if  the  earth 
revolved  around  the  sun  was  known  at  a  very  early  date.  Tycho 
Brahe  observed  them  in  order  to  discover  whether  they  were  sen- 
sibly fixed  in  the  sky  or  not.  So  far  as  his  observations  went  they 
did  not  change  their  positions  during  the  year.  He  inferred  from  this 
that  the  earth  remained  fixed  and  that  the  sun  moved.  His  error 
was  due  to  the  fact  that  his  observations  were  not  sufficiently  accurate 
to  show  the  slight  displacement  which  the  stars  have.  His  observa- 
tions were  made  shortly  before  the  invention  of  the  telescope  and 
he  could  not  measure  the  minute  angles  through  which  the  stars  were 
displaced.  In  fact,  their  distances  are  so  great  and  the  parallactic 
displacements  are  so  small  that  the  nineteenth  century  was  well 
advanced  before  astronomers  succeeded  in  finding  any  stars  with 
measurable  parallaxes.  At  the  present  time,  in  spite  of  the  great 
precision  of  modern  instruments,  the  parallaxes  of  only  50  or  60 
stars  have  been  directly  measured,  but  these  50  or  60  prove  in  the 
most  rigorous  fashion  that  the  earth  actually  revolves  around  the  sun. 


46 


ASTRONOMY 


Revolution  of  the  Earth  Proved  by  Aberration  of  Light.    The 

earliest  direct  proof  that  the  earth  revolves  around  the  sun  was  made 
in  1728  by  the  discovery  of  what  is  called  the  aberration  of  light. 


Fig.  18.    The  Apparent  Direction  of  the  Stars  Is  Slightly  Changed  by  the  Motion 
of  the  Earth  across  the  Path  of  the  Rays  of. Light  from  Them 

Suppose  rain  is  falling  vertically  and  one  stands  still  in  it. 
Then  it  appears  to  him  that  it  is  coming  straight  down.  Suppose 
he  walks  rapidly  through  it;  then  it  seems  to  meet  him  obliquely, 
striking  him  in  the  face.  Suppose  he  rides  through  it  rapidly;  then 
it  seems  to  meet  him  more  obliquely.  The  angle  at  which  it  seems 
to  strike  him  depends  upon  the  speed  with  which  it  falls,  and  the 

speed  with  which  he  goes  across  the  line  of 
its  motion. 

If  one  moves  at  right  angles  to  the  di- 
rection of  the  light  rays  a  similar  phenom- 
enon is  observed.  In  Fig.  18,  suppose  AB 
is  the  direction  of  the  earth's  motion.  Sup- 
pose the  continuous  lines  which  meet  it  at 
right  angles  are  the  direction  of  the  rays 
of  light  from  a  distant  star.  Because  of 
the  earth's  motion  along  AB  the  rays  of 
light  from  the  star  will  appear  to  come  in 
along  the  dotted  lines.  This  causes  the 
star  to  be  apparently  displaced  in  the  di- 
A  star  Apparently  De-  rection  in  which  the  observer  is  going.  It 
follows  from  the  velocity  of  light  and  the 
velocity  that  the  earth  must  have  if  it 
goes  around  the  sun,  that  this  displacement  should  be  about  20 
seconds  of  arc.  This  is  a  quantity  which  is  easily  observable  and 
does  not  depend  upon  the  distance  of  the  stars.  The  problem 


Fig.  19. 

scribes  Yearly  a  Small  Curve  in 
the  Sky  Because  of  the  Ab- 
erration of  Its   Light 


ASTRONOMY  47 

is  to  determine  by  observations  whether  the  star  is  thus  displaced 
or  not. 

In  Fig.  19,  let  ABCD  represent  the  orbit  of  the  earth  and  s  the 
actual  position  of  a  star.  Suppose  the  earth's  motion  is  in  the  direc- 
tion ABCD.  When  the  earth  is  at  A  the  star  will  be  displaced 
by  the  aberration  in  the  direction  in  which  the  earth  moves  and 
will  be  seen  at  a.  Similarly,  when  the  earth  is  at  B,  C,  and  D, 
the  star  will  be  seen  at  6,  c,  and  d,  respectively.  That  is,  while  the 
earth  describes  its  orbit  the  star  will  describe  an  apparent  small  curve 
in  the  sky  whose  radius  is  about  20  seconds.  This  is  the  fact  which 
was  discovered  in  1728  by  the  English  astronomer  James  Bradley. 
The  direction  and  the  amount  of  the  displacement  agree  precisely 
with  the  theory  that  the  earth  revolves  around  the  sun,  and  con- 
stitute an  absolute  proof  of  its  motion. 

Revolution  of  the  Earth  Proved  by  the  Spectroscope.  The  spec- 
troscope is  an  instrument  by  means  of  which  it  is  possible  to  deter- 


Fig.  20.     When  the  Earth  Is  at  A,  It  Is  Approaching  the  Star  S.     When  the 

Earth  Is  at  B,  It  Is  Receding  from  S.     The  Spectroscope  Shows 

This  Motion  and  Proves  the  Revolution 

mine  whether  the  observer  is  approaching  or  receding  from  any 
luminous  object.  It  enables  him  not  only  to  determine  whether  he  is 
approaching  or  receding,  but  also  the  relative  speed.  This  is  all  that 
we  need  to  know  of  the  spectroscope  at  the  present  time.  The 
discussion  of  the  construction  of  this  instrument  and  its  uses  will 
be  treated  in  connection  with  the  sun. 

If  the  earth  is  the  center  of  the  system  and  the  stars  are  fixed, 
the  spectroscope  will  show  that  we  neither  approach  nor  recede  from 
them.  On  the  other  hand,  if  the  sun  is  the  center  and  the  earth 
revolves  around  it,  the  spectroscope  will  show  that  at  certain  times 
of  the  year  we  are  approaching  the  stars  and  that  at  other  times  we 
are  receding  from  the  same  stars.  In  Fig.  20,  let  S  represent  the  sun 
and  AB  the  earth's  orbit.  Suppose  the  direction  of  the  earth's 


48  ASTRONOMY 

motion  is  indicated  by  the  arrow.  Let  s  represent  the  position  of  a 
distant  fixed  star.  When  the  earth  is  at  A  it  will  be  approaching  the 
star  and  six  months  later  when  it  is  at  B  it  will  be  receding  from  it 
at  the  same  rate. 

In  order  to  determine  by  this  method  whether  the  sun  or  the 
earth  is  the  center  it  is  necessary  to  make  spectroscopic  observations 
of  stars  at  the  proper  times.  It  is  clear  from  the  figure  that  it  is 
most  convenient  to  take  stars  in  or  near  the  plane  of  the  earth's  orbit. 
Now,  the  actual  observations  made  on  thousands  of  stars  show  us 
that  when,  according  to  the  theory  that  the  earth  revolves  around 
the  sun,  we  should  be  approaching  the  stars  we  are  actually  approach- 
ing them,  and  that  we  recede  when  the  theory  demands  that  we 
should  be  receding.  In  this  way  the  spectroscope  proves  with  cer- 
tainty that  the  earth  revolves  around  the  sun.  It  not  only  gives  us 
this  fact  but  it  determines  for  us  the  speed  with  which  it  goes.  Since 
the  length  of  the  year  is  known  and  the  speed  is  determined  by  means 
of  the  spectroscope,  we  can  compute  the  whole  circumference  of  the 
earth's  orbit,  and  consequently  the  distance  from  the  earth  to  the 
sun.  This  is  only  one  of  many  methods  of  determining  this  distance, 
and  it  is  significant  that  the  result  agrees  very  closely  with  that 
found  by  all  the  other  methods. 

Shape  of  the  Earth's  Orbit.  It  was  assumed  in  the  first  discus- 
sion of  the  subject  that  the  orbit  of  the  earth  is  circular.  Obviously, 
this  is  the  simplest  closed  curve.  If  the  orbit  is  a  circle  with  the  sun 
at  its  center,  then  the  sun  will  be  at  the  same  distance  from  the  earth 
throughout  the  year  and  consequently  will  be  always  of  the  same 
apparent  size.  It  is  clear  that  an  object  looks  smaller  the  farther 
one  is  away  from  it,  but  if  the  orbit  of  the  earth  is  not  a  circle  then 
its  distance  from  the  center  will  vary  during  the  year  and  the  apparent 
size  of  the  sun  will  change  correspondingly. 

It  is  found  from  the  actual  observations  of  the  apparent  diameter 
of  the  sun  that  it  changes  throughout  the  year.  At  one  time  it  is 
nearly  two  per  cent  greater  than  it  is  six  months  from  that  time. 

The  shape  of  the  earth's  orbit  and  the  way  in  which  the  earth 
moves  in  it  can  be  determined  rather  easily  from  the  observations. 
Suppose,  in  Fig.  21,  S  represents  the  sun  and  the  curve  E1E2E3Et 
the  orbit  of  the  earth  (the  elongation  is  greatly  exaggerated).  Sup- 
pose an  observation  is  made  when  the  sun  is  in  the  direction  Eft. 


ASTRONOMY  49 

A  convenient  scale  can  be  chosen  and  the  line  Efi  laid  down.  Sup- 
pose at  a  later  date  the  sun  is  seen  in  the  direction  E2S.  The  line 
can  be  laid  down  and  the  distance  E2S  determined  by  the  apparent 
size  of  the  sun.  If  the  apparent  diameter  of  the  sun  is  smaller  when 
observed  at  E2  than  at  El}  then  E2  is  farther  from  S  than  is  Et.  If 
the  diameter  is  one  per  cent  smaller,  then  the  distance  is  one  per  cent 
greater,  and  similarly  for  any  other  differences.  In  this  fashion  the 
point  E2  is  located.  In  a  similar  way  the  positions  of  the  lines 
E3S  and  E4S  and  the  distances  are  determined,  and  the  points 
which  represent  the  position  of  the  earth  are  laid  down.  The  curve 
drawn  through  them  will  represent  the  orbit  of  the  earth  in  shape, 
the  position  of  the  sun  in  its  interior,  and  the  way  in  which  the 
earth  moves  in  its  orbit.  Such  observations  as  these  have  shown 
that  the  orbit  of  the  earth  is  an 
ellipse,  and  that  the  sun  is  at  one 
of  its  foci.  See  Fig.  5. 

It  is  also  found  that  the  earth 
moves  in  its  orbit  so  that  the 
line  from  the  sun  to  it  sweeps 
over  equal  areas  in  equal  inter- 
vals of  time.  For  example,  if  the 

Fig.  21.     The  Line  Joining  the  Earth  and 

time    required    for    the    earth    tO  the  Sun  Sweeps  Over  Equal  Areas  in 

Equal  Intervals  of  Time 

move  from  El  to  E2  is  the  same 

as  that  required  for  it  to  move  from  E3  to  E4,  then  the  area  E^SE^ 

is  equal  to  the  area  EZSE4. 

Obliquity  of  the  Ecliptic.  The  sun,  moon,  and  stars  as  seen 
from  the  earth  appear  to  be  on  a  great  sphere  enclosing  them  all, 
which  is  called  the  celestial  sphere.  Since  they  are  at  very  different 
distances  from  us  they  are  not  actually  on  any  sphere,  but  only  seem 
to  be  on  one.  In  describing  their  directions  from  us  it  is  permissible 
to  regard  them  as  being  on  this  celestial  sphere.  The  apparent  path 
of  the  sun  in  its  apparent  yearly  motion  around  the  earth  is  a 
great  circle  on  the  celestial  sphere  which  is  called  the  ecliptic.  It  is 
not  the  path  of  the  sun  but  the  projection  of  its  apparent  path  on 
the  celestial  sphere;  or,  it  may  be  defined  as  the  circle  in  which  the 
plane  of  the  earth's  orbit  cuts  the  celestial  sphere. 

The  plane  of  the  earth's  equator  cuts  the  celestial  sphere  in 
another  great  circle  known  as  the  celestial  equator.  The  angle  between 


50  ASTRONOMY 

the  celestial  equator  and  the  ecliptic  is  called  the  obliquity  of  the 
ecliptic. 

In  Fig.  22,  the  line  from  the  sun  to  P  is  parallel  to  the  earth's 
axis.  The  circle  CABV  represents  the  celestial  equator,  which  is 
parallel  to  the  earth's  equator,  and  the  circle  SAWV  represents  the 
ecliptic,  which  is  in  the  plane  of  the  earth's  orbit.  As  seen  from 
the  earth  the  sun  moves  along  the  ecliptic  from  west  to  east,  indi- 
cated in  the  figure  by  the  arrow.  The  place  where  the  sun  crosses 
the  equator  from  south  to  north,  indicated  by  V  in  the  figure,  is 
called  the  vernal  equinox,  and  the  place  where  it  crosses  from  north 

to  south,  indicated  by  A  in  the 
figure,  the  autumnal  equinox. 
The  earth  is  at  a  when  the  sun 
seems  to  be  at  the  point  A.  And 
similarly  the  earth  is  at  w,  v,  s 
when  the  sun  appears  to  be  at 
W,  V,  S.  The  axis  of  the  earth 
is  perpendicular  to  the  plane  of 
the  equator  and  keeps  always  par- 
allel to  its  initial  direction  while 
the  earth  moves  around  the  sun. 
Precession  of  the  Equinoxes. 
The  ecliptic  is  a  curve  which  is 

almost  absolutely  fixed  in  the  sky.  The  only  changes  in  it  are  due 
to  the  slight  irregularities  in  the  motion  of  the  earth  produced  by 
the  attractions  of  the  other  planets.  On  the  other  hand,  the  celestial 
equator  is  not  fixed  because  the  plane  of  the  earth's  equator  is 
changed  rather  rapidly  by  the  attraction  of  the  sun  and  moon  on 
the  equatorial  bulge  of  the  earth.  The  angle  between  the  plane  of 
the  earth's  equator  and  the  plane  of  the  ecliptic,  or  the  obliquity  of 
the  ecliptic,  remains  fixed;  but  the  position  of  the  plane  shifts  so 
that  the  points  A  and  V  go  westward  on  the  ecliptic  to  ^and  Vi. 
Since  A  moves  in  the  direction  opposite  to  that  of  the  apparent 
motion  of  the  sun  the  change  is  called  "precession."  The  rate  is  about 
50.2  seconds  of  arc  annually,  from  which  it  follows  that  the  equinoxes 
will  make  a  complete  revolution  only  after  25,800  years  have  elapsed. 
In  spite  of  the  fact  that  the  precession  is  very  slow,  it  was  discovered 
by  the  ancient  Greeks  three  centuries  before  the  beginning  of  the 


ASTRONOMY 


51 


Christian  Era<     This  is  an  evidence  of  the  perfection  which   astro- 
nomical science  had  attained  among  them. 

As  we  shall  see,  the  seasons  depend  upon  the  obliquity  of  the 
ecliptic.  If  we  should  define  as  the  year  for  ordinary  purposes  the 
time  it  takes  the  sun  to  go  from  any  apparent  point  on  the  ecliptic 
back  to  the  same  point  again,  we  should  find  as  the  consequence  of 
the  precession  of  the  equinoxes  that  the  sun  is  not  at  the  vernal 
equinox  at  the  same  time  on  succeeding  years.  For  example,  if 
some  time  it  is  found  that  the  sun  is  at  the  vernal  equinox  precisely 
at  the  beginning  of  the  year  it  will  pass  the  vernal  equinox  again 


Fig.  23.     The  Altitude  of  the  Pole  of  the  Sky  Equals  the 
Latitude  of  the  Observer 

slightly  before  the  end  of  the  year.  Consequently,  with  this  sort  of 
year  we  should  have  continually  shifting  seasons.  Therefore,  the 
year  which  is  adopted  for  ordinary  civil  purposes  is  the  time  it  takes 
the  sun  to  go  from  the  vernal  equinox  V  around  to  the  vernal 
equinox  Vlt  Fig.  22,  which  is  little  less  than  a  complete  revolution. 
Using  this  year,  the  seasons  always  remain  fixed  with  respect  to  it. 
Causes  of  the  Seasons.  The  direct  cause  of  the  seasons  is  the 
varying  amount  of  light  and  heat  received  from  the  sun  per  day. 
It  is  a  matter  of  common  observation  that  in  the  summer  time  the 
sun  shines  more  hours  per  day  than  in  the  winter  time  and  that  at 
midday  its  rays  fall  more  nearly  perpendicularly.  The  problem 
before  us  is  to  discover  the  laws  of  these  changes  on  the  basis  of 


52  ASTRONOMY 

the  motions  of  the  earth,  and  to  apply  them  to  a  determination  of 
the  extent  of  the  changes.  As  a  preliminary  to  this  discussion  it 
will  be  necessary  to  determine  the  relation  between  the  latitude  of 
the  observer  and  the  altitude  of  the  pole  in  the  sky,  as  he  sees  it, 
and  that  of  the  equator  where  it  crosses  his  meridian.  In  Fig.  23, 
let  the  circle  E  represent  the  earth  and  PP'  its  axis  of  rotation. 
Suppose  the  observer  is  at  0;  then  his  latitude  is  /.  The  posi- 
tion of  the  pole  in  the  sky  is  that  point  on  the  celestial  sphere 
towards  which  the  line  P'P  points.  The  celestial  sphere  is  so 
remote  that  a  line  from  0  towards  the  pole  will  be  parallel 
to  P'P.  The  equator  will  be  at  right  angles  to  P'P.  The  hor- 
izon of  the  observer  at  0  is  indicated  in  the  figure.  The  angle 
between  the  plane  of  the  horizon  and  the  line  from  the  observer  to 
the  pole  is  at  a,  and  from  the  observer  to  the  equator  is  b.  The 
sides  of  the  angle  a  are,  respectively,  perpendicular  to  the  sides  of  the 
angle  /,  and  it  follows  therefore  from  plane  geometry  that  a— I. 
That  is,  the  distance  of  the  north  pole  of  the  sky  above  the  north 
point  of  the  horizon  in  degrees  is  always  equal  to  the  latitude  of  the 
observer.  It  can  be  seen  from  the  figure  that  the  angle  b=  (90°  — /). 
That  is,  the  latitude  of  the  equator  on  the  meridian  above  the  south 
point  of  the  horizon  in  degrees  is  equal  to  90  degrees  minus  the  lati- 
tude of  the  observer. 

As  an*  example  of  these  results  it  may  be  noticed  that  if  an 
observer  is  on  the  earth's  equator  where  his  latitude  is  zero,  the 
north  pole  of  the  sky  is  at  the  north  point  of  the  horizon;  and  the 
point  where  the  equator  cuts  the  meridian  is  directly  over  his  head. 
On  the  other  hand,  if  he  were  at  the  earth's  pole  so  that  his  latitude 
were  90°,  the  celestial  pole  would  be  directly  over  his  head  while  the 
equator  would  be  on  the  horizon. 

In  Fig.  24,  0  represents  the  position  of  the  observer  and  N,  E,  S, 
and  W  the  north,  east,  south,  and  west  points  of  his  horizon.  The 
latitude  of  the  observer  is  such  that  the  north  pole  of  the  sky  is  at 
P  and  the  equator  at  A  WEE.  Now,  because  of  the  rotation  of 
the  earth,  the  sun  has  an  apparent  diurnal  motion  from  east  to  west, 
completing  a  circuit  of  the  sky  in  one  day.  Suppose  the  sun  is  at 
the  vernal  equinox,  the  point  V  in  Fig.  22.  Then  it  is  on  the  celestial 
equator  and  it  is  clear  that  the  diurnal  motion  is  along  the  circle 
E  A  WH  in  the  direction  indicated  by  the  arrow.  This  is  a  great 


ASTRONOMY  53 

circle  and  is  bisected  by  the  horizon.  Consequently,  when  the  sun  is 
on  the  celestial  equator  it  is  half  of  the  twenty-four  hours  above  the 
horizon,  and  the  remaining  half  below  it. 

Besides  this  diurnal  motion  the  sun  has  a  slow  motion  along 
the  ecliptic.  After  it  passes  the  point  V  in  Fig.  22,  it  is  north 
of  the  equator,  and  it  reaches  its  greatest  distance  north  at  S,  when 
it  is  23.5  degrees  north  of  the  equator.  Now  consider  Fig.  24, 
which  shows  the  circles  of  the 
diurnal  motion.  When  the  sun  is 
23.5  degrees  north  of  the  equator 
it  moves  on  the  circle  BKIF.  It 
is  above  the  horizon  while  it 
moves  over  the  arc  FBK,  and 
below  it  while  it  moves  over  the 
arc  KIF.  It  is  clear  from  the 
figure  that  it  is  above  the  horizon 
considerably  more  than  one-half 
of  the  24  hours.  Six  months  from 

this  time  the  SUn  will  have  moved        Fig.  24.     The  Diurnal  Circles  of  the  Sun  at 

i   ,       , !  .     ,    Trr      n  •»-,.       nn  Different  Distances  from  the 

arOUnd  tO  the  point  W  Of  Fig.  22,  Celestial  Equator 

when  it  will  be  23.5  degrees  south 

of  the  equator.  At  this  time  its  diurnal  motion  is  along  the  circle 
DCLG.  It  is  above  the  horizon  while  it  describes  the  arc  DCL, 
and  below  it  while  it  describes  LGD.  It  is  clear  from  the  figure 
that  in  this  case  the  sun  is  above  the  horizon  much  less  than  one-half 
of  the  24  hours. 

To  summarize  the  matter,  we  may  state  that  the  sun  is  above 
the  horizon  one-half  of  the  24  hours  when  it  is  on  the  celestial  equa- 
tor, whatever  the  latitude  of  the  observer  may  be.  It  is  on  the  celes- 
tial equator  twice  a  year  at  the  vernal  and  autumnal  equinoxes. 
When  it  is  north  of  the  equator,  moving  from  the  vernal  to  the  au- 
tumnal equinox,  it  is  above  the  horizon  more  than  one-half  of  each 
24  hours.  (These  statements  should,  of  course,  be  reversed  if  they 
are  to  be  made  for  observers  in  the  southern  hemisphere.)  In  the  six 
months  while  it  is  south  of  the  equator,  viz,  while  it  is  moving  from 
the  autumnal  equinox  to  the  vernal  equinox,  it  is  above  the  horizon 
less  than  one-half  of  each  24  hours.  This  variation  in  the  length  of  sun- 
light per  day  is  one  of  two  chief  causes  in  the  changes  in  the  seasons. 


54  ASTRONOMY 

The  second  important  reason  why  the  seasons  change  is  that  the 
direction  of  the  sun's  rays  at  noon,  for  instance,  varies  throughout 
the  year.  In  Fig.  24  the  horizon  SENW  is  given  and  it  is  seen  that 
the  sun's  rays  strike  the  surface  of  the  earth  at  the  angle  AOS  when 
the  sun  is  on  the  equator.  When  it  is  north  of  the  equator  they 
strike  nearer  to  the  perpendicular  at  the  angle  BOS;  and  when  it  is 
south  of  the  equator  they  strike  more  obliquely  at  the  angle  COS. 
It  is  easy  to  show  that  the  nearer  the  perpendicular  the  sun's 
rays  strike  the  more  they  heat  the  surface.  In  Fig.  25,  AB  represents 

the  cross-section  of  a  certain 
beam  of  light.  If  the  rays 
should  strike  the  surface  per- 
pendicularly they  would  all  fall 
a  on  an  area  whose  distance 

Fig.  25.     When  the  Sun's  Rays  Strike  the  Earth  i  i    u        A  n        r>    ±    •£ 

Obliquely  They  Are  Spread  Out  over  a  Large         acrOSS    WOUld    be    AB.       But    if 
Area  and  Their  Heating  Effect  Is  Small  ,.  ,         ,  ,      J    .,        ,.  „ 

they  should  strike  the  surface 

obliquely,  as  is  indicated  in  the  figure,  then  the  same  rays  would  be 
spread  over  the  larger  area  aB.  Consequently,  being  spread  over  a 
larger  area,  they  would  illuminate  and  heat  it  less  than  when  spread 
over  the  smaller  area.  Therefore,  when  the  sun  is  high  in  the  sky 
at  noon  it  heats  the  surface  more  than  it  does  when  its  rays  fall 
obliquely.  This  matter  is  illustrated  by  the  fact  that  the  temperature 
is  higher  at  noon,  when  the  sun's  rays  fall  almost  perpendicularly, 
than  it  is  when  the  sun  is  rising  or  setting. 

Relative  Amounts  of  Sunlight  in  Different  Latitudes.  It  is 
often  supposed  that  the  equatorial  part  of  the  earth  is  that  which 
is  not  only  hottest,  but  which  receives  the  most  hours  of  sunlight.  It 
is  clear  from  the  discussion  above  that  the  northern  hemisphere 
receives  more  light  than  the  average  in  the  summer  and  less  in  the 
winter,  and  it  is  at  least  conceivable  that  these  two  extremes  exactly 
balance.  A  mathematical  discussion  shows  that  they  do  exactly 
balance  for  all  latitudes. 

In  order  to  illustrate  the  matter  let  us  take  the  two  extreme 
cases,  viz,  where  the  observer  is  at  the  earth's  equator  and  where 
he  is  at  its  pole.  Fig.  26  represents  the  positions  of  the  diurnal  circles 
relative  to  the  horizon  when  the  observer  is  at  the  earth's  equator. 
When  the  sun  is  on  the  celestial  equator  it  rises  at  E  and  travels 
along  the  diurnal  circle  E  Air  II,  during  which  time  it  is  above  the 


ASTRONOMY 


55 


horizon.  It  is  seen  from  the  figure  that  this  is  exactly  one-half  of  its 
whole  diurnal  circle.  Similarly,  whether  it  is  north  of  the  equator 
and  moving  along  the  diurnal  circle  FBKI,  or  south  of  the  equator 
and  moving  along  the  diurnal  circle  DCLG,  it  is  also  exactly  one- 
half  of  each  24  hours  above  the  horizon.  Therefore,  at  the  earth's 
equator  the  sun  shines  exactly  one-half  of  the  time. 

But  \vhen  the  observer  is  at  the  earth's  pole,  the  celestial  pole 
is  directly  over  his  head,  Fig.  27,  and  the  equator  coincides  with 
his  horizon.  Consequently,  the  sun  shines  only  when  it  is  north  of 
the  equator,  which  is  one-half  of  the  year.  Therefore,  in  this  case 
also  the  sun  shines  one-half  of  the  whole  year. 

While  the  total  number  of  hours  of  sunlight  per  year  are  the 
same  at  the  equator  and  at  the  pole,  as  has  just  been  shown,  and 


Fig.  2G.     Diurnal  Circles  for  an  Observer 
at  the  Earth's  Equator 


Diurnal  Circles  for  an  Observer 
at  the  Earth's  Pole 


also  in  all  other  latitudes  as  can  be  shown  by  proper  mathematical 
discussion,  it  is  to  be  remarked  that  their  distribution  is  very  differ- 
ent. At  the  earth's  equator  the  sun  shines  an  equal  number  of  hours 
during  each  day  throughout  the  year.  At  the  pole  the  sunshine  is 
continuous  for  six  months.  It  follows  from  this  that  the  variation  in 
the  seasons  is  much  greater  at  the  pole  than  it  is  at  the  equator.  If 
one  were  to  take  into  account  the  refraction  of  light,  which  elevates 
the  sun  a  distance  about  equal  to  its  diameter  when  it  is  on  the  hori- 
zon, it  would  be  found  that  the  total  number  of  hours  during  which 
the  sun  is  visible  from  the  pole  is  greater  than  that  during  which  it  is 
visible  from  the  equator. 


56  ASTRONOMY 

While  the  number  of  hours  of  sunshine  in  a  year  is  the  same  for 
all  points  on  the  earth  it  must  not  be  supposed  that  the  total  amount 
of  sunlight  received  is  the  same  for  all  points.  On  the  earth's  equator 
twice  each  year  the  sun  passes  through  the  zenith  and  every  day 
passes  near  to  it.  There  is,  therefore,  a  time  each  day  when  its 
rays  strike  nearly  perpendicularly  on  the  surface.  On  the  other 
hand,  at  the  pole  the  sun  never  gets  more  than  23.5  degrees  above 
the  horizon  and  its  rays  always  strike  very  obliquely.  Consequently, 
the  amount  of  light  and  heat  received  at  the  equator  are  very  much 
greater  than  at  the  pole.  The  amount  received  at  the  equator  in  a 
year  is  about  the  same  as  it  would  be  if  the  sun  stood  still  17  degrees 
above  the  horizon,  for  the  whole  year.  The  amount  received  at  the 
pole  for  the  whole  year  is  about  the  same  as  it  would  be  if  the  sun 
stood  still  at  an  angle  of  5.8  degrees  above  the  horizon.  It  follows 
from  this  that  at  the  equator  the  amount  of  light  and  heat  received 
are  a  little  more  than  three  times  that  received  at  the  pole. 

If  it  were  not  for  the  obliquity  of  the  ecliptic,  the  pole  would 
receive  infinitely  little  sunlight  because — except  for  the  refraction — 
the  sun  would  always  be  exactly  on  the  horizon.  Thus,  it  follows 
that  the  obliquity  of  the  ecliptic  causes  a  higher  mean  temperature 
at  the  pole  than  it  would  otherwise  have.  At  the  equator,  on  the 
other  hand,  the  sun  passes  through  the  zenith  but  twice  in  the  year. 
Consequently,  the  equator  receives  less  sunlight  and  heat  than  it 
would  if  the  obliquity  of  the  ecliptic  were  zero.  Hence,  a  conse- 
quence of  the  obliquity  of  the  ecliptic  is  that  the  equatorial  regiong 
are  cooler  and  the  polar  regions  warmer  than  they  would  otherwise 
be;  that  is,  the  obliquity  of  the  ecliptic  has  a  tendency  to  equalize 
the  earth's  climate,  taken  as  a  whole. 

An  interesting  fact  in  this  connection  is  that,  theoretically, 
the  highest  temperatures  would  not  be  found  exactly  at  the  equator. 
When  the  sun  is  on  the  equator  it  passes  through  the  observer's 
zenith.  This  happens,  however,  on  but  one  day,  for  it  rapidly  passes 
away  from  the  equator.  This  is  made  clear  in  Fig.  22,  since  the  sun 
is  on  the  earth's  equator  when  it  is  at  V,  which  it  quickly  crosses. 
On  the  other  hand,  when  the  sun  is  near  S,  Fig.  22,  its  distance  north 
of  the  equator  changes  very  slowly.  For  some  weeks  it  does  not  vary 
enough  to  make  any  material  difference.  For  an  observer  who  is 
just  far  enough  north  of  the  equator  so  that  it  then  passes  through 


ASTRONOMY  57 

his  zenith,  it  will  be  above  his  horizon  more  than  one-half  of  each  24 
hours,  and  will  pass  very  near  his  zenith  each  day.  At  this  time  he 
is  receiving  more  light  and  heat  than  is  ever  received  in  a  similar 
length  of  time  by  an  observer  at  the  earth's  equator.  It  follows  from 
this  that  theoretically  the  temperature  should  be  highest  near  the 
points  which  are  approximately  23.5  degrees  north  and  south  of 
the  earth's  equator. 

Lag  of  the  Seasons.  From  the  astronomical  point  of  view 
the  times  when  the  sun  is  at  V  and  A,  Fig.  22,  are  corresponding 
seasons.  It  is  found  from  the  observations  that  the  sun  is  at  the 
vernal  equinox  on  March  21  and  at  the  autumnal  equinox  on  Sep- 
tember 23.  (The  dates  on  which  it  passes  the  equinoxes  can  vary  a 
day  or  so  from  those  just  given  because  of  the  shifting  leap  year.) 
It  is  perfectly  clear  from  the  point  of  view  of  the  climate  that  March 
21  and  September  23  are  not  corresponding  times  in  the  year.  The 
reason  is  the  seasons  lag,  as  we  say.  There  is  a  corresponding  lag 
in  the  day  which,  being  simpler,  will  be  first  discussed. 

From  the  standpoint  of  the  amount  of  light  and  heat  received, 
nine  o'clock  in  the  morning  and  three  o'clock  in  the  afternoon  are 
corresponding  times  of  day.  But  almost  invariably  the  temperature 
is  higher  at  three  o'clock  than  it  is  at  nine  o'clock.  The  reason  is 
that  at  nine  o'clock  the  earth  is  receiving  more  heat  than  it  radiates. 
This  continues  until  noon  when  the  maximum  amount  is  received. 
But  at  this  time  it  is  also  receiving  more  than  it  radiates  and  con- 
tinues to  do  so  until  the  increase  of  its  temperature  and  the  decrease 
in  the  amount  received  cause  the  radiation  to  equal  exactly  that 
which  is  received.  After  that  the  temperature  begins  to  fall.  But 
under  normal  weather  conditions  this  occurs  considerably  after  noon. 
The  time  after  noon  at  which  the  highest  temperature  is  reached  is 
called  the  lag  of  the  noon.  There  is  a  corresponding  lag  in  the  time 
of  lowest  temperature  at  night.  Of  course,  when  the  sun  has  set  no 
light  and  heat  are  received  from  it  directly  until  morning,  but  it  is 
farthest  below  the  horizon  at  midnight.  Instead  of  this  being  the 
time  of  the  lowest  temperature,  as  a  rule  the  temperature  steadily 
falls  from  sundown  until  almost  sunrise  in  the  morning. 

Now  consider  the  seasons.  As  the  sun  mounts  higher  and  higher 
in  the  sky  in  the  spring  so  that  more  and  more  heat  is  received  daily, 
the  earth  gets  considerably  warmer  both  because  of  the  greater 


58  ASTRONOMY 

number  of  hours  of  sunshine  and  also  because  of  the  high  altitude 
of  the  sun  at  noon.  During  the  spring  months,  for  example,  April 
and  May,  the  earth  receives  more  heat  in  the  northern  hemisphere 
than  is  lost  by  radiation,  and  the  temperature  rises.  This  continues 
until  about  the  21st  of  June  when  the  sun  arrives  at  the  point  S, 
Fig.  22,  which  is  its  greatest  distance  north  of  the  equator.  But  at 
this  time  the  maximum  amount  of  heat  is  received  and  this  is  more 
than  that  which  is  radiated.  Consequently,  the  mean  temperature 
continues  to  rise  for  some  time  after  the  21st  of  June.  It  becomes 
stationary  only  when  the  temperature  rises  to  such  a  point  that  the 
increased  radiation  and  the  decreased  amount  received  exactly 
balance.  In  moderate  latitudes  this  lag  amounts  to  some  weeks. 

If  the  earth  had  no  atmosphere  and  if  it  radiated  the  heat  as 
fast  as  it  was  received  there  would  be  no  lag  of  the  seasons.  Atmos- 
phere is  one  of  the  causes  of  the  lag  of 
the  seasons.  The  more  it  absorbs  light 
and  heat  as  they  come  to  the  earth,  and 
prevents  their  escaping  as  the  earth 
radiates  them  out,  the  more  the  seasons 
will  lag.  It  is  a  matter  of  common  ob- 
servation  that  there  is  a  greater  lag  to 

Beort£°Earfh?acOrnbiticit          the  seasons  in  low  altitudes,  especially 
where  the  atmosphere  is  moist,  than  there 
is  on  the  high  and  dry  plateaus. 

Effect  of  the  Eccentricity  of  the  Earth's  Orbit  upon  the  Seasons. 
In  the  discussion  up  to  this  point  it  has  been  assumed  tacitly  that 
the  orbit  of  the  earth  around  the  sun  is  a  circle.  As  explained  above, 
it  is  an  ellipse  and  the  earth  is  about  three  per  cent  nearer  at  the 
point  nearest  the  sun  than  it  is  when  most  remote.  Consequently, 
the  amount  of  light  and  heat  received  depends  to  some  extent  upon 
the  varying  distance  of  the  earth  from  the  sun.  It  should  be  said, 
however,  that  this  is  not  so  important  a  cause  as  that  discussed  above. 
There  is  a  very  interesting  indirect  result  of  the  eccentricity 
of  the  earth's  orbit,  viz,  that  the  seasons  in  the  northern  and  southern 
hemispheres  are  not  of  equal  length.  In  Fig.  28,  V  represents  the 
position  of  the  earth  when  the  sun  is  at  the  vernal  equinox,  and  A 
its  position  when  the  sun  is  at  the  autumnal  equinox.  The  point  P 
is  the  earth's  position  when  it  is  nearest  the  sun.  It  is  almost  midway 


ASTRONOMY  59 

between  A  and  V,  but  a  little  nearer  V  than  A.  It  follows  from  the 
law  of  areas  that  the  earth  will  pass  from  A  through  P  to  V  in  a 
shorter  time  than  is  required  for  it  to  pass  from  V  through  Q  to  A. 
If  we  count  the  days  from  March  21  to  September  23  it  is  found  that 
the  summer,  from  the  astronomical  point  of  view,  in  the  northern 
hemisphere  is  186  days  and  the  winter,  viz,  the  time  from  September 
23  to  March  21,  is  179  days.  The  more  exact  figures  are:  the  length 
of  the  summer  in  the  northern  hemisphere  is  186J  days,  and  the 
winter  179  days.  That  is,  because  of  the  eccentricity  of  the  earth's 
orbit,  the  summer  is  7 J  days  longer  than  the  winter.  In  the  southern 
hemisphere  the  conditions  are  reversed. 

One  might  suppose  from  this  that  there  were  peculiar  climatic 
advantages  in  the  northern  hemisphere.  The  facts  are,  however, 
that  the  same  amount  of  light  and  heat  are  received  in  the  year  at 
any  point  in  the  northern  hemisphere  as  are  received  at  any  point 
having  an  equal  latitude  in  the  southern  hemisphere.  The  increase 
in  the  length  of  the  summer  in  the  northern  hemisphere  is  exactly 
offset  by  the  greater  distance  from  the  sun  during  this  time,  and  its 
nearness  to  the  sun  in  the  winter  in  the  northern  hemisphere  is 
exactly  compensated  by  the  fact  that  the  winter  is  shorter.  The 
more  exact  statement  is  that  equal  latitudes  in  the  northern  and 
southern  hemispheres  receive  exactly  the  same  amount  of  light  and 
heat  in  corresponding  parts  of  any  seasons.  The  chief  difference  is 
that  in  the  northern  hemisphere  the  tendency  is  for  the  climate  to  be 
somewhat  more  uniform,  since,  when  the  rays  strike  nearest  to  the 
perpendicular,  the  earth  is  farthest  from  the  sun.  The  conditions 
are  reversed  in  the  southern  hemisphere.  The  fact,  however,  that 
there  is  so  much  more  water  in  the  southern  hemisphere  than  there 
is  in  the  northern,  probably  more  than  counterbalances  these  astro- 
nomical causes  for  an  equable  climate  in  the  northern  hemisphere. 

The  eccentricity  of  the  earth's  orbit  slowly  changes  and  the 
direction  of  its  major  axis  PQ  also  chan  es  because  of  the  attrac- 
tions of  the  other  planets  for  it.  Likewise  it  was  seen  above  that 
there  is  a  precession  of  the  equinoxes,  so  that  the  line  A  V  does  not 
remain  fixed.  It  follows  from  this  that  not  only  does  the  elongation 
of  the  orbit  of  the  earth  change,  but  also  the  positions  of  the  lines 
PQ  and  AV  change  relative  to  each  other.  In  about  10,000  years 
from  now  the  conditions  will  be  the  opposite  of  those  we  have  at 


60  ASTRONOMY 

present.  At  that  time  the  summers  in  the  northern  hemisphere 
will  be  shorter  than  the  winters  and  more  heat  will  be  received  per 
day  than  during  the  summers  in  the  southern  hemisphere.  In  the 
course  of  a  very  long  time,  counted  by  tens  of  thousands  of  years, 
the  eccentricity  of  the  earth's  orbit  will  be  greater  than  it  is  at  present, 
though  now  it  is  decreasing  and  will  decrease  very  slowly  for  a  long 
time. 

It  has  been  supposed  that  an  unequal  distribution  of  the  light 
and  heat  received  from  the  sun  throughout  the  year  are  favorable  to 
glaciation.  An  English  geologist,  Croll,  suggested,  as  an  explanation 
of  the  ice  ages  which  the  earth  has  experienced,  that  they  were 
due  to  the  fact  that  at  certain  times  the  northern  hemisphere  had 
long,  cold  winters  and  short,  hot  summers.  He  supposed  that  the 
accumulation  of  ice  and  snow  in  the  winter  time,  under  those  circum- 
stances, would  be  so  great  that  they  would  not  be  melted  in  the 
summer.  This  theory  has  been  abandoned  because,  according  to 
it,  the  intervals  between  the  ice  ages  would  be  counted  by  hundreds 
of  thousands  of  years,  whereas  geologists  find  they  were  much  closer 
together  than  this.  Likewise  there  have  been  ice  ages  very  probably 
at  the  same  time  in  both  the  northern  and  southern  hemispheres. 
According  to  this  theory,  when  the  conditions  are  favorable  to 
glaciation  in  one  hemisphere  they  are  unfavorable  to  it  in  another, 
and  glaciation  should  not  be  simultaneous  both  north  and  south  of 
the  equator. 


CTA2.    CLUSTER    AND    NEBULA   IN   CYGNUS 
Taken  with  a  10-inch  Bruce  lens.      The  streak  at  the  top  of  the  picture  was  made  by  a  large    meteor 


ASTRONOMY 

PART  II 


THE   CONSTELLATIONS 

Problem  of  Locating  the  Constellations.  The  most  careless 
observer  of  the  sky  has  noticed  that  the  stars  are  not  uniformly 
spread  over  it.  Almost  everyone  is  familiar  with  the  Big  Dipper 
and  the  Pleiades,  otherwise  known  as  the  Little  Dipper.  These 
natural  groups  of  stars  were  given  names  in  antiquity  by  early 
observers  and  are  called  constellations.  Their  names  often  strike  us 
as  being  most  fantastic  and  far-fetched.  Many  of  them  are  the 
names  of  wild  animals.  For  example,  we  have  the  Great  Bear, 
the  Lesser  Bear,  the  Lion,  the  Eagle,  the  Leopard,  etc. 

If  the  sky  is  watched  for  a  few  hours  it  is  observed  that  these 
groups  of  stars  move  across  it  from  the  east  toward  the  west.  The 
fact  that  they  are  not  fixed  in  the  sky  leads  to  some  little  difficulty 
in  describing  their  positions.  Suppose  an  observer  watches  them  a 
few  nights  until  he  finds  how  they  move  throughout  the  night  and 
knows  where  they  appear  at  any  time  of  the  night.  If  he  then  ceases 
to  observe  them  for  a  few  months  and  again  returns  to  his  observa- 
tions, he  will  find  things  are  quite  different.  Those  stars  which  at 
his  first  observations  were  visible  high  in  the  sky  late  in  the  night 
are  a  few  months  later  visible  early  in  the  evening.  Thus,  he  finds 
that  not  only  do  the  stars  change  their  positions  in  the  sky  during 
the  night  but  that  on  successive  nights  these  positions  are  not 
the  same.  There  is  a  continual  shift  throughout  the  year. 

It  follows  from  these  changing  positions  of  the  stars  and  the 
necessity  in  certain  astronomical  work  of  locating  them  with  the 
very  highest  degree  of  precision,  that  it  is  necessary  to  adopt  some 
machinery  for  describing  their  positions.  As  was  stated  above,  all 
the  heavenly  bodies  seem  to  be  seen  on  a  great  sphere.  This  sphere, 

Copyright,  1912,  by  American  School  of  Correspondence. 


62 


ASTRONOMY 


surrounding  the  visible  universe  and  having  the  earth  as  its  cenl 
is  called  in  astronomy  the  celestial  sphere.  The  problem  of  tl 
astronomer  is  to  locate  the  positions  of  the  heavenly  bodies  on  thij 
sphere,  which  is  in  many  respects  similar  to  the  problem  of  locating 
the  position  of  a  place  on  the  earth,  which  for  ordinary  geographic 
purposes  may  be  regarded  as  a  sphere.  From  the  standpoint  of 
geometry  the  two  problems  are  exactly  the  same.  They  appear  to 
us  to  be  slightly  different  because  in  the  case  of  the  earth  we  are  on 
the  outside  and  in  case  of  the  celestial  sphere  we  are  on  the  inside. 
But  in  representing  the  celestial  sphere  by  a  globe  we  are  on  the 
outside,  and  this  is  sometimes  a  little  confusing.  However,  by  a 

little  use  of  the  imagination  the 
identity  of  the  two  problems  can 
be  seen,  and  our  knowledge  of 
what  is  done  in  geography  will 
assist  in  understanding  how  the 
corresponding  problem  is  solved  in 
astronomy. 

Geographical  System.  The  lines 
on  the  earth  by  means  of  which 
we  locate  places  fall  into  two  fun- 
damentally distinct  systems:  (1) 
there  are  the  equator  and  the 
system  of  small  circles  parallel  to 
it;  (2)  there  are  the  great  circles 
which  pass  through  the  poles  of  the  earth  and  cut  the  equator  at 
right  angles.  The  circles  to  be  defined  are  the  equator  (after  which 
all  the  parallel  circles  are  given)  and  the  particular  great  circle  per- 
pendicular to  the  equator  from  which  we  count. 

In  locating  the  position  of  a  place  on  the  earth,  we  give  its 
distance  north  or  south  of  the  equator,  called  its  latitude,  and  its 
distance  east  or  west  of  some  selected  meridian,  called  its  longitude. 
The  meridian  is  selected  for  its  convenience,  the  ones  in  most 
common  use  being  those  through  the  Royal  Observatory  at  Green- 
wich, England,  the  one  through  the  Naval  Observatory  at  Washing- 
ton, and  those  in  other  countries  passing  through  their  national 
observatories.  The  position  of  Chicago,  for  example,  is  about  41°  50' 
north  of  the  equator  and  78°  22'  west  of  the  meridian  of  Greenwich. 


Tig.  29.  The  Latitude  and  Longitude 
Circles  on  the  Earth 


ASTRONOMY 


63 


In  Fig.  29,  EAB  represents  the  equator  and  PPr  the  poles. 
Suppose  the  meridian  PAP'  is  the  fundamental  meridian  from  which 
longitudes  are  counted.  Consider  a  point  at  C.  The  latitude  is  the 
arc  BC,  and  the  longitude  is  the  arc  AB  measured  along  the  equator. 
It  is  to  be  noted  that  it  must  bo  measured  along  the  equator 
because  the  latitude  circle  through  C  is  a  small  circle. 

Horizon  System.  In  defining  the  circles  of  this  system  it  is 
simpler  to  start  with  the  zenith  than  with  the  horizon.  The  zenith  is 
the  point  overhead  where  the  plumb-line  extended  upward  pierces 
the  celestial  sphere.  The  nadir  is  the  point  below  180°  from  the 
zenith.  The  horizon  is  the  great  circle  of  the  celestial  sphere  90° 
from  the  zenith  and  nadir.  This  is  the  astronomical  horizon  and  it 
may  differ  in  particular  instances  considerably  from  the  sensible 
horizon  wrhich  is  determined  by 
the  apparent  union  of  earth  and 
sky,  and  depends,  obviously, 
upon  all  sorts  of  irregularities. 
Tin-  horizon  corresponds  to  the 
equator  in  the  Geographical  Sys- 
tem. The  small  circles  parallel 
to  the  horizon,  corresponding  to 
the  circles  of  latitude  in  the 
Geographical  System,  are  called 
'parallels  of  attitude. 

The  circles  corresponding  to 
the  meridians  in  the  Geograph-       Fig'  30'    The  Horizon  System  of  Circle9 
ical  System  are  the  circles  on  the  celestial  sphere  which  pass  through 
the  zenith  and  nadir  and  cut  the  horizon  perpendicularly.     They 
are  called  vertical  circles  becaus3  they  cut  the  horizon  vertically. 

The  position  of  a  point  on  the  celestial  sphere  is  determined  by 
giving  its  distance  above  or  below  the  horizon  and  its  distance  corre- 
sponding to  longitude.  The  distance  from  the  horizon  is  called  the 
altitude,  plus  if  above  and  minus  if  below. 

The  vertical  circle  from  which  the  other  distances  are  counted 
is  the  one  passing  through  the  zenith  and  the  south  point.  This 
second  distance,  which  is  called  azimuth,  is  counted  westward  from 
the  south  point  around  to  the  foot  of  the  vertical  circle  through  the 
object  in  question.  Thus,  in  Fig.  30,  suppose  C  is  a  celestial  object 


64  ASTRONOMY 

whose  altitude  and  azimuth  we  wish  to  give.  Its  distance  above 
the  horizon  measured  along  the  vertical  circle  is  BC,  which  is  its 
altitude.  Its  azimuth  is  the  arc  starting  from  S  measured  westward 
through  W  and  N  to  B,  which,  in  the  present  example,  is  somewhat 
greater  than  180°.  In  this  respect  the  scheme  differs  a  little  from 
the  Geographical  System,  where  longitudes  are  counted  both  east- 
ward and  westward,  and  azimuth  only  westward.  There  is  nothing 
fundamental  in  this  method,  but  it  is  found  simpler  to  count  it  all  the 
way  around  to  360  degrees,  rather  than  to  be  under  the  necessity  of 
always  stating  whether  it  is  counted  eastward  or  westward. 

The  reason  that  azimuth  is  counted  westward  instead  of  east- 
ward is  that  the  stars  in  their  diurnal  motions  go  from  east  to  west 
across  the  sky.  Counting  the  azimuth  westward,  we  find  that  it 
increases  as  the  night  goes  on.  When  a  star  is  on  the  meridian  its 
azimuth  is  zero  and  as  it  passes  west  of  the  meridian  its  azimuth 
steadily  increases.  If  the  azimuth  were  counted  in  the  other  direction 
from  the  south  point,  then  the  azimuth  of  a  star,  as  it  crosses  the 
meridian,  would  pass  from  zero  to  359  degrees,  and  then  continually 
decrease.  The  inconvenience  of  such  a  method  as  this  is  at  once 
evident. 

Equator  System.  In  defining  the  Equator  System  it  is  simplest 
to  start  with  the  celestial  pole.  In  this  work  reference  will  be  contin- 
ually made  to  the  north  pole,  since  we  live  in  the  northern  hemisphere 
of  the  earth,  but  corresponding  statements  can  in  every  case  be  made 
for  the  southern  pole.  The  celestial  pole  is  the  center  of  the  diurnal 
circles  which  the  stars  describe  (see  Fig.  ll);  or  it  is  the  place 
where  the  earth's  axis  extended  northward  pierces  the  celestial  *phm\ 

In  Fig.  31,  let  0  be  the  position  of  the  earth  and  P  and  P'  the 
positions  of  the  celestial  poles.  The  celestial  equator  is  the  great 
circle  on  the  celestial  sphere  90  degrees  from  the  celestial  pole,  or 
it  is  the  great  circle  in  which  the  plane  of  the  earth's  equator  cuts 
the  celestial  sphere.  The  small  circles  parallel  to  the  celestial  equator 
are  called  parallels  of  declination.  In  Fig.  31  VEB  represents  the 
equator  and  DCF  a  parallel  of  declination. 

The  celestial  equator  corresponds  to  the  earth's  equator  in  the 
Geographical  System,  and  the  parallels  of  declination  correspond  pre- 
cisely to  the  parallels  of  latitude.  In  fact,  these  circles  on  the  celestial 
sphere  are  parallel  to  the  corresponding  ones  on  the  earth. 


ASTRONOMY  65 

The  circles  which  correspond  to  the  meridians  on  the  earth  pass 
through  P  and  P',  Fig.  31,  and  are  perpendicular  to  the  equator. 
They  are  called  hour  circles  for  reasons  which  will  be  explained 
presently.  The  fundamental  hour  circle  from  which  distances  are 
counted  is  the  one  which  passes  through  the  vernal  equinox,  repre- 
sented by  V  in  Fig.  31. 

The  distance  north  or  south  of  the  equator,  corresponding  to 
latitude  on  the  earth,  is  declination;  positive  if  north,  negative  if 
south.  The  distance  corresponding  to  longitude  on  the  earth  is 
right  ascension,  which  is  counted  eastward  from  the  vernal  equinox 
along  the  equator  to  the  foot  of  the  hour  circle  through  the  object. 
This  differs  from  longitude  on 
the  earth  in  that  it  is  counted 
only  in  one  direction. 

If  one  wishes  to  give  the 
position  of  C,  Fig.  31,  in  the 
Equator  System,  he  gives  its 
declination,  which  is  the  arc  BC, 
and  its  right  ascension,  which  is 
the  arc  VB,  measured  eastward 
from  V  through  E  to  B. 

Since  the  earth  rotates  on  its        Fig  31    The  Equator  System  of  Co_ 
axis  from  west  to   east,  the  sky 

apparently  rotates  from^as^to  west.  The  point  V  is  not  a  fixed 
,  point  on  the  apparent  sky,  as  one  looks  at  it.  It  rises  in  the  east  at 
E  daily,  goes  across  the  sky  to  the  west  and  sets  at  W,  passing  around 
to  E  again.  The  star  at  C  passes  along  the  declination  circle  through 
D  around  to  F  and  back  to  C  daily.  Its  highest  altitude  is  when  it 
is  on  the  meridian  at  D.  It  was  shown  above  that  the  altitude  of 
the  equator  on  the  meridian  is  90  degrees  minus  the  latitude  of  the 
observer.  Consequently,  the  highest  altitude  of  a  star  is  90  degrees 
minus  the  latitude  of  the  observer  plus  the  declination  of  the  star. 
For  example,  if  an  observer  is  40  degrees  north  of  the  equator  and 
he  observes  a  star  whose  declination  is  twenty  degrees  north,  he  finds 
that  when  it  crosses  its  meridian  its  altitude  is  90°— 40°+ 20°  =70°. 

Its  lowest  altitude  is  when  it  is  at  F;  on  the  point  where  the 
equator  cuts  the  antimeridian  NP',  it  is  90  degrees  minus  the  lati- 
tude of  the  observer  below  the  horizon.  The  lowest  altitude  of  a 


66  ASTRONOMY 

star  in  its  diurnal  motion  is  therefore  90  degrees  minus  the  latitude 
of  the  observer,  plus  the  declination  of  the  star.  For  example,  in 
the  problem  given  above  the  lowest  altitude  of  the  star  is  —90°+ 
40°+ 20°=  -30°,  or  30  degrees  below  the  horizon.  In  this  way  it  is 
found  that,  for  an  observer  in  latitude  40  degrees,  the  highest  altitude 
of  the  sun,  when  it  is  at  the  summer  solstice  23.5  degrees  north  of  the 
equator,  is  73.5  degrees,  and  its  lowest  altitude  below  the  horizon  is 
26.5  degrees.  In  the  winter  time,  when  the  declination  of  the  sun  is 
23.5  degrees  south,  it  is  found  in  a  similar  way  that  its  highest  altitude 
in  the  day  for  an  observer  in  latitude  40  degrees  north  is  20.5  degrees 
and  its  lowest  altitude  is  —73.5  degrees. 

The  reason  that  the  circles  passing  through  P  perpendicular  to 
the  equator  are  called  hour  circles  is  that  they  move  from  east  to 
west  across  the  sky  in  their  diurnal  motions,  making  a  circuit  in  24 
hours.  Consequently,  if  they  are  drawn  one  hour  apart  they  will 
cross  the  meridian  one  after  another  at  intervals  of  an  hour.  For 
this  reason  it  is  customary  to  count  right  ascension  in  hours  rather 
than  in  degrees,  though  the  relation  is  simple.  The  360  degrees 
around  the  celestial  equator  are  divided  into  24  hours,  from  which  it 
follows  that  one  hour  is  equal  to  15  degrees. 

It  is  readily  seen  from  this  how  easy  the  problem  of  determining 
the  right  ascension  of  the  stars  is  if  one  has  a  clock  and  a  telescope 
mounted  in  the  plane  of  the  meridian.  Suppose  he  keeps  the  tele- 
scope fixed  and  makes  a  record  of  the  time  the  stars  pass  across  its 
field,  which  is  the  time  they  pass  the  meridian.  Suppose  his  clock  ^ 
is  set  so  that  it  registers  zero  hours  when  the  vernal  equinox  passes 
the  meridian,  and  that  it  is  marked  to  run  from  zero  to  24.  Then 
if  a  star  passes  at  one  o'clock  its  right  ascension  is  one  hour,  and 
similarly  for  any  other  time.  This  is,  in  fact,  the  way  the  right 
ascensions  of  the  stars  are  determined.  At  the  same  time  their 
declination  can  also  be  determined.  If  it  is  found  how  high  they 
are  above  the  horizon  when  they  pass  the  meridian,  their  declination 
is  at  once  given  because  their  declination  is  equal  to  their  altitude 
minus  the  altitude  of  the  equator.  If  they  are  north  of  the  equator, 
and  consequently  have  an  altitude  greater  than  the  equator,  this 
comes  out  a  positive  result.  On  the  other  hand,  if  they  are  south 
of  the  equator  their  declination  comes  out  negative.  These  results 
agree  with  the  definitions  of  positive  and  negative  declination  given 


ASTRONOMY 


67 


above.  Since  the  altitude  of  the  equator  is  90  degrees  minus  the 
latitude  of  the  observer,  it  follows  that  the  declination  of  the  star 
is  its  observed  altitude  plus  the  latitude  of  the  observer  minus  90 
degrees. 

Ecliptic  System.  The  ecliptic  has  been  defined  as  the  apparent 
path  of  the  sun  around  the  celestial  sphere.  It  is  a  great  circle  cutting 
the  celestial  equator  at  the  vernal  and  autumnal  equinoxes  and 
inclined  to  it  by  an  angle  of  23.5  degrees.  In  Fig.  32,  KEMW 
represents  the  celestial  equator  and  LVJA  the  ecliptic,  which 
cuts  the  equator  in  V  and  A.  As  before,  SWNE  represents  the 
plane  of  the  horizon. 

The  parallels  to  the  ecliptic, 
which  are  not  given  in  the  dia- 
gram, are  called  the  parallels  of 
latitude.  The  distance  north  or 
south  of  the  ecliptic  is  called  the 
latitude.  The_great  circles  perpen- 
dicular to  the  ecliptic  are  called 


celestial  meridians.     The  funda- 


mental one  from  which  distances 


along  the  ecliptic  are  counted  is 

the  one  passing  through  the  vernal 
equinox.     It  follows  that  the  fun- 


Fig.  32. 


The  Relation   of   Horizon,  Ecliptic, 
and  'Equator 


damental  hour  circle  and  the  fundamental  celestial  meridian  intersect 
at  the  vernal  equinox.  They  do  not,  of  course,  coincide  because  the 
former  is  perpendicular  to  the  celestial  equator  and  the  latter  to  the 
ecliptic.  The  distance  from  this  fundamental  celestial  meridian 
counted  eastward  along  the  ecliptic  to  the  foot  of  the  celestial  meridian 
through  the  object  is  called  the  celestial  longitude.  It  is  counted  east- 
ward until  the  object  is  reached  even  up  to  360  degrees.  Since  the 
vernal  equinox  goes  around  the  sky  in  the  diurnal  motions  of  the 
heavens,  as  has  been  explained  above,  the  Ecliptic  System  revolves  in  a 
similar  fashion,  but  in  this  case  the  motion  with  respect  to  the  horizon 
is  considerably  more  complex  than  in  the  case  of  the  Equator  System. 
For  one-half  of  the  360  degrees  the  ecliptic  is  above  the  equator,  and 
for  the  other  one-half  it  is  below  it.  Consequently,  during  one-half 
of  24  hours  the  ecliptic  cuts  the  meridian  at  a  greater  altitude  than 
the  equator,  and  during  the  other  half  at  a  lesser  altitude.  The 


68  ASTRONOMY 

ecliptic  cuts  the  meridian  in  24  hours  at  all  the  altitudes  at  which 
the  sun  crosses  the  meridian  in  a  whole  year.  The  reason  for  this  is, 
of  course,  that  the  sun  passes  around  the  ecliptic  once  in  a  year. 

Comparison  of  Systems.  If  one  person  were  to  describe  to 
another  verbally  where  certain  stars  could  be  seen  it  would  evidently 
be  the  simplest  for  him  to  give  their  altitude  and  azimuth.  He 
would  immediately  look  into  the  sky  and  locate  the  objects.  But 
if  he  were  to  write  to  a  person  in  another  place  serious  difficulties 
would  arise.  In  the  first  place,  the  one  who  was  to  observe  the 
celestial  objects  would  see  them  at  a  different  time.  In  general  it 
would  be  both  at  a  different  time  of  the  day  and  a  different  time  of 
the  year.  Consequently,  the  description  would  fail  unless  additionaj 
data  were  given,  because,  as  was  stated  in  the  beginning  of  the  dis- 
cussion of  the  Horizon  System,  the  altitude  and  the  azimuth  of  the 
stars  not  only  change  during  the  night  but  for  a  given  time  of  night 
change  through  the  year. 

There  is  another  reason  why  the  Horizon  System  would  not 
be  simple  unless  the  observer  were  to  look  at  the  place  where  the 
person  was  who  gave  him  the  description.  This  second  reason  is 
that  the  position  of  an  observer's  horizon  depends  upon  his  location 
on  the  earth.  This  follows  obviously  from  the  fact  that  the  zenith, 
and  therefore  indirectly  the  horizon,  depends  upon  the  direction  of 
the  plumb  line  of  the  observer.  Altogether,  therefore,  in  order  to  use 
the  Horizon  System  as  a  means  of  describing  the  location  of  celestial 
objects  it  is  necessary  not  only  to  give  their  altitude  and  azimuth 
but  also  the  time  of  day,  the  day  of  the  year,  and  the  position  of 
the  observer.  Obviously,  for  catalogue  purposes,  this  system  is 
inconvenient.  In  a  word,  this  system  of  reference  points  and  lines 
slides  on  a  celestial  sphere. 

The  Equator  System  is  distinguished  by  the  fact  that  its  refer- 
ence points  and  lines  are  fixed  among  the  stars.  The  position  of  the 
celestial  pole  and  the  celestial  equator  are  altogether  independent  of 
the  observer's  position.  Likewise  the  vernal  equinox,  from  which  the 
right  ascensions  are  counted,  is  independent  of  the  observer's  posi- 
tion, the  time  of  the  day,  or  the  time  of  the  year.  A  slight  correc- 
tion to  this  statement  is  necessary  because  of  the  precession  of  the 
equinoxes  as  explained  above.  This  is  a  very  slow  process  and  need 
not  be  considered  in  the  present  connection. 


ASTRONOMY  69 

The  Equator  System  is  fixed  on  the  celestial  sphere  and  is  well 
adapted  for  cataloguing  purposes.  To  locate  a  star  by  it  we  need 
only  to  give  its  right  ascension  and  declination.  That  locates  it 
permanently  and  for  any  place  and  time.  In  order  for  an  observer 
to  see  the  object  he  must  calculate  in  some  way  where  it  will  be  as 
seen  from  his  position  at  the  time  he  wishes  to  view  it.  The  Equator 
System  is  the  one  actually  used  in  all  catalogues.  The  right  ascen- 
sions and  declinations  are  determined  essentially  as  described  above. 

The  Longitude  System  is  similar  to  the  Equator  System  in 
that  it  is  fixed  on  the  celestial  sphere.  If  a  point  is  given  in  terms  of 
the  celestial  latitude  and  longitude  it  is  uniquely  located,  but  this 
system  is  not  in  so  common  use  as  the  equatorial  because  it  does  not 
connect  so  easily  with  the  observations  made  by  the  telescope  fixed 
in  the  plane  of  the  meridian  in  connection  with  the  astronomical 
clock.  Its  principal  uses  are  in  describing  the  positions  of  the  sun, 
moon,  and  planets,  which  never  depart  very  far  from  the  ecliptic. 

Determination  of  Right  Ascension  of  Meridian  at  Any  Time. 
Since  the  catalogues  use  the  Equator  System  and  the  observers 
depend  upon  the  Horizon  System,  it  is  necessary  in  order  to  use  a 
catalogue  in  making  observations  to  establish  the  connection  between 
the  two  systems.  Suppose  the  right  ascension  of  a  certain  star  is 
given  and  it  is  desired  to  know  whether  it  is  visible  at  the  time  in 
question  or  not.  If  its  right  ascension  is  the  same  as  that  of  the 
meridian  it  will  be  on  the  meridian  and  will  be  visible  provided  it  is 
not  too  near  the  southern  pole  of  the  sky.  On  the  other  hand,  if 
its  right  ascension  is  12  hours  from  that  of  the  meridian  it  will  be  on 
the  opposite  side  of  the  earth  and  invisible  unless  it  is  near  the  north 
pole  of  the  sky  so  as  to  be  above  the  horizon.  The  right  ascension 
of  the  star  being  given  in  the  catalogue,  the  problem  of  determining 
whether  it  is  visible  or  not  is  reduced  to  that  of  finding  the  right 
ascension  of  the  meridian  at  any  time.  We  shall  now  consider  this 
problem. 

The  sun  is  found  by  observation  to  be  at  the  vernal  equinox 
on  March  21  of  each  year.  (This  date  may  vary  by  a  day  because 
of  the  accumulated  errors  which  are  adjusted  every  four  years  by  the 
leap  year.)  It  moves  eastward  along  the  ecliptic  at  a  nearly  uniform 
rate,  the  variation  from  uniformity  being  expressed  by  the  law  of 
areas.  For  present  purposes  it  is  sufficiently  exact  to  suppose  it 


70  ASTRONOMY 

moves  eastward  uniformly  along  the  equator,  which  is  represented 
by  the  circle  ME  AW  in  Fig.  33.  Since  it  makes  the  circuit  of  the 
heavens  in  12  months,  and  since  the  circumference  is  divided  into 
24  hours  of  right  ascension,  it  follows  that  the  sun  moves  eastward 
from  the  vernal  equinox  about  two  hours  each  month.  Consequently, 
to  find  the  right  ascension  of  the  sun,  it  is  necessary  only  to  count  the 
number  of  months  from  March  21  to  the  day  in  question  and  to 
multiply  by  two.  Thus,  on  June  21,  which  is  three  months  after 
the  sun  passes  the  vernal  equinox,  the  right  ascension  of  the  sun  is 
approximately  six  hours.  On  October  21,  which  is  approximately 
seven  months  after  the  sun  passes  the  vernal  equinox,  the  right 
ascension  of  the  sun  is  14  hours. 

We  wish,  however,  the  right  ascension  of  the  meridian  at  the 

time  in  question  instead  of  the 
right  ascension  of  the  sun.  We 
shall  make  the  determination  of 
the  right  ascension  of  the  sun 
the  first  step  in  solving  this  prob- 
lem. If  it  is  the  stars  we  wish 
to  observe  they  necessarily  will 
be  seen  at  night  and  the  most 
convenient  time  is  in  the  early 
part  of  the  night.  Suppose, 
therefore,  that  as  a  practical 
problem  we  determine  the  right 
ascension  of  the  meridian  at 

eight  o'clock  on  any  night.  By  the  method  described  above  the 
right  ascension  of  the  sun  is  found,  whose  position  is  indicated  by  s 
in  Fig.  33.  Now  the  right  ascension  is  counted  eastward.  Conse- 
quently, tjie  right  ascension  of  the  meridian  M  is  equal  to  that  of 
the  sun  jmis  the  angular  distance  sWM.  If  it  is  8  o'clock  p.  M.  the  sun 
has  passed  the  meridian  eight  hours  and  the  arc  sWM  is  eight  hours. 
For  example,  on  June  21  the  right  ascension  of  the  sun  is  six  hours 
and  the  right  ascension  of  the  meridian  at  8  P.  M.  is  6+8=  14  hours. 
If  one  wished  to  locate  the  vernal  equinox,  which  would  be  less  con- 
venient to  use,  it  would  be  found  six  hours  west  of  the  sun. 

Similarly,  on  October  21  the  right  ascension  of  the  sun  being  14 
hours,  the  right  ascension  of  the  meridian  at  8  P.  M.  is  22  hours. 


ASTRONOMY  71 

In  the  two  examples  the  stars  that  are  on  the  meridian  at  the  times 
in  question  are,  respectively,  those  whose  right  ascensions  are  14  hours 
and  those  whose  right  ascensions  are  22  hours.  The  problem  is 
solved  in  an  exactly  similar  manner  for  any  other  day  and  time  of  day. 
Application  of  Declination  to  Location  of  Stars.  It  is  evident 
that  the  visibility  of  a  group  of  stars  depends  not  only  upon  their 
right  ascension  but  also  upon  their  declination.  In  Fig.  24,  it  was 
shown  that  when  the  sun  is  north  of  the  equator  it  is  visible  more 
than  one-half  of  the  24  hours, -while  if  it  is  south  of  the  equator  it  is 
visible  less  than  one-half  of  the  24  hours.  That  is,  when  the  sun  is 
north  of  the  equator  it  is  visible  at  a  greater  distance  from  the  merid- 
ian than  it  is  when  it  is  south 
of  the  equator.  Since  the 
diurnal  motion  of  the  sun  is  par- 
allel to  the  diurnal  motions  of 
the  stars  the  same  thing  is  true 
of  them.  The  difference  is  that 
the  stars  always  have  sensibly 
the  same  declinations  and  any 
statement  made  for  them  at 
one  time  holds  for  all  time. 
Another  difference  is  that  the 
stars  extend  all  the  way  from  Fig.  34.  The  Diumai  Circles  of  the  stars. 

rmp     nnlp»     fn    thp»    ntVipr         T^ina^      Those  near  the   North  Pole   ares  always  above 

,  pole  to  me  otner.  the  horizon  and  those  near  the  Sout-h  Pole 

which  are  on  the  equator,  half 

of  which  is  above  the  horizon,  are  visible  only  if  they  are  less  than 
six  hours  east  or  west  of  the  meridian. 

For  practical  observations  it  is  necessary  that  the  stars  should 
be  some  little  distance  above  the  horizon,  though  theoretically  they 
are  visible  until  they  arrive  at  the  horizon.  Stars  which  are  north 
of  the  equator  are  visible  even  though  their  distances  from  the  merid- 
ian east  or  west  are  somewhat  greater  than  six  hours,  the  amount 
depending  on  how  far  they  are  north.  In  Fig.  34,  it  is  seen  that 
those  which  are  near  enough  the  pole;  viz,  in  sector  NQP,  are  always 
visible.  The  pole  P  is  the  center  of  the  diurnal  circles  and  the  dis- 
tance NP  is  equal  to  the  distance  PQ.  It  was  shown  above  that 
NP  is  equal  to  the  latitude  of  the  observer.  Therefore,  those  stars 
whose  distance  from  the  pole  of  the  sky  is  less  than  the  latitude  of 


72  ASTRONOMY 

the  observer  are  always  visible  to  him.  Around  the  southern  pole 
of  the  sky  there  is  a  similar  region  of  equal  area,  RP'R,  in  which  the 
stars  are  never  visible.  If  a  star's  declination  is  so  far  south  that  its 
distance  from  the  southern  pole  is  less  than  the  latitude  of  the  obser- 
ver then  he  will  never  see  it. 

If  an  observer  is  at  the  earth's  equator  all  the  stars  are  visible 
to  him  in  the  course  of  time.  Those  which  are  at  the  poles  of  the 
heavens  are  on  the  north  or  south  horizons.  Those  which  are  at 
the  celestial  equator  rise  in  the  east,  pass  through  the  zenith,  and 
set  in  the  west.  But  if  an  observer  were  at  the  pole  of  the  earth 
the  pole  of  the  heavens  would  be  at  his  zenith  and  the  celestial 
equator  on  his  horizon.  Therefore,  only  one-half  of  the  celestial 
sphere  would  ever  be  visible  to  him.  The  diurnal  motions  of  the 
stars  would  be  in  circles  parallel  to  the  horizon. 

Origin  of  Constellations.  Nearly  all  our  constellations  (groups 
of  stars)  have  been  handed  down  to  us  from  prehistoric  times.  They 
had  their  origin,  probably,  in  Babylonia  and  Egypt  and  were  trans- 
mitted to  us  through  the  Greeks  and  the  Arabians.  Many  of  the 
names  of  the  stars  as  well  as  of  the  reference  points  and  lines  are  of 
Arabic  origin,  having  been  translated  into  this  tongue  from  the 
more  ancient  ones.  Thus  the  words  zenith,  nadir,  horizon,  azimuth, 
etc.,  are  Arabic.  The  names  of  most  of  the  bright  stars  are  also 
Arabic.  Those  observers  who  originally  named  the  constellations 
lived  in  the  northern  hemisphere,  and  there  were  certain  stars  in  the 
vicinity  of  the  south  pole  of  the  sky  which  were  not  visible  to  them. 
Consequently,  in  this  part  of  the  sky  the  stars  were  given  no  names. 
There  were  also  certain  places  in  the  northern  heavens  where  the 
stars  were  not  very  conspicuous,  which  were  not  covered  by  the  con- 
stellations of  the  ancients.  To  fill  up  these  gaps  a  few  constella- 
tions have  been  added  in  modern  times. 

The  outlines  of  the  constellations  are  extremely  irregular  and 
the  stars  situated  in  them  generally  give  no  suggestion  whatever  of 
the  names  which  have  been  assigned  to  them.  By  the  wildest 
stretch  of  the  imagination  it  is  not  possible  for  us  to  see  that  the  stars 
which  constitute  Leo  have  any  resemblance  to  the  outline  of  a  lion, 
and  equally  dissimilar  to  their  names  are  the  other  constellations. 

A  list  of  the  constellations  is  given  in  Table  I.  In  the  left- 
hand  column  their  right  ascensions  are  given  and  at  the  top  of  the 


TABLE  I 
List  of  Constellations  with  Right  Ascensions  and  Declinations 


Dec. 
R/AT^ 

+  90°  to  +50° 

+  50°  to  +25° 

+  25°toO° 

0°  to  -  25° 

-  25°  to  -  50° 

+  50°  to  -90° 

I-II 

Cassiopeia 
46 

Andromeda 
18 
Triangulum 
5 

Pisces  18 
Aries  17 

Cetus  37 

Phoenix  32 
Apparatus 
Sculptoris  13 

(Phoenix) 
Hydrus  18 

III-IV 

Perseus  46 

Taurus  58 

Eridanus  64 

(Eridanus) 

Horologium 
11 
Reticulum  9 

V-VI 

Camelopar- 
dalus  36 

Auriga  35 

Orion  58 
Gemini  33 

Lepus  18 

Columba  15 

Dorado  16 
Pictor  14 
Mons  Mensa 
12 

VII-VIII 

Lynx  28 

Canis 
Minor  8 
Cancer  15 

Canis  Major 
27 
Monoceros 
12 

Argo  Navis 
149 

Piscis  Volans 
9 

IX-X 

Leo  Minor  15 

Leo  47 

Hydra  49 
Sextans  5 

XI-XII 

Ursa  Major 
53 



Coma  Ber- 
inices  20 

Crater  15 
Corvus  8 

Centaurus  6 

Chameleon 
13 

XIII-XIV 

Canes  Vena- 
tici  15 
Bo"tes  36 

Virgo  39 

Lupus  34 

Crux  13 
Musca  15 

XV-XVI 

LJrsa  Minor 
23 

Corona  Bo- 
realis  19 
Hercules  65 

Serpens  25 

Libra  23 

Norma  14 

Circinus  10 

XVII-XVIII 

Draco  80 

Lyra  18 

Aquila  37 
Sagitta  5 

Scorpio  34 
Ophiuchus 
46 

Aral5 

Triangulum 
Australis  11 
Apus  8 

XIX-XX 

Cygnus  67 

Vulpecula 
23 
Delphinus 
10 

Sagittarius 

48 

Corona 
Australis  18 

Telescopium 
16 
Pavo  37 
Octans  22 

XXI-XXI1 

Cepheus  44 

Lacerta  16 

Equuleus 
5 

Capricornus 
22 

Piscis         / 
Australis  16 

Indus  15 

XXIII-XXIV 

Pegasus 
43 

Aquarius 
36 

Grus  30 

Toucana  22 

74  ASTRONOMY 

columns  are  their  declinations.  In  connection  with  each  constella- 
tion a  number  will  be  observed  which  indicates  the  number  of  con- 
spicuous stars  in  the  constellation.  The  names  of  certain  constella- 
tions are  printed  in  italics.  These  are  the  stars  which  lie  along  the 
ecliptic  and  are  called  the  signs  of  the  zodiac.  The  ancients  always 
spoke  of  the  sun  as  being  in  a  certain  sign  or  constellation,  as  in 
Scorpio,  Sagittarius,  etc.  It  is  easy  for  us  to  determine  at  what  time 
of  the  year  the  sun  is  in  a  given  constellation.  For  example,  from 
the  list  of  constellations  we  see  that  the  right  ascension  of  Scorpio 
is  XVII  — XVIII  hours.  The  sun  has  a  right  ascension  of  18  hours 
at  18/2=9  months  after  March  21,  or  December  21. 

Suppose  it  is  required  to  find  at  what  time  of  the  year  Leo  is 
visible  at  8  P.  M.  From  the  table  it  is  seen  that  its  right  ascension 
is  ten  hours.  If  it  is  to  be  on  the  meridian  the  right  ascension  of  the 
meridian  is  therefore  ten  hours  on  the  day  in  question.  The  sun 
being  eight  hours  west,  and  right  ascension  being  counted  eastward, 
the  right  ascension  of  the  sun  will  be  10—8=2  hours.  The  right 
ascension  of  the  sun  is  two  hours  on  April  21.  Therefore,  the  constel- 
lation Leo  is  on  the  meridian  April  21  at  8  P.  M.  In  this  way  the 
table  can  be  used  to  find  at  what  time  of  the  year  any  constella- 
tion is  on  the  meridian  at  eight  o'clock  at  night,  or  at  any  other 
hour  of  the  night.  It  should  be  used  in  locating  the  stars,  espe- 
cially in  connection  with  the  star  maps. 

Maps  I,  II,  III,  and  IV  give  all  the  constellations  except 
those  within  40  degrees  of  the  south  pole  of  the  sky,  which  are 
not  visible  in  the  latitude  of  the  United  States.  Map  I  shows 
those  around  the  north  pole  of  the  heavens.  It  is  made  so  it  can 
be  used  by  determining  first  the  right  ascension  of  the  meridian  at 
the  time  in  question;  and  second  by  turning  the  map  so  that  this 
hour  of  right  ascension  which  is  marked  on  its  margin,  is  above  the 
pole ;  then  the  map  is  held  up  so  that  its  center  is  seen  by  the  eye  in 
the  direction  of  the  pole  of  the  sky.  When  the  map  is  turned  around 
in  this  way  to  the  sky  the  positions  of  the  stars  located  on  it  are  the 
same  relatively  as  those  in  the  sky. 

Suppose,  for  example,  that  the  time  the  observer  uses  it  is 
May  21,  at  8  P.M.  The  right  ascension  of  the  sun  on  this  date  is 
four  hours,  and  of  the  meridian  at  this  time  12  hours.  Consequently, 
the  hour  circle  marked  12  in  the  map  must  be  held  directly  above 


ASTRONOMY 


75 


MAP  I 
Constellations  Around  North  Pole  of  the  Heavens 


ASTRONOMY 


77 


3       3 


tj 

"      ^ 

.  0 


V 


\ 


1 

•  § 


•i 


r  « 
i   . 


--t  •• 


1 

u 


V 


78 


ASTRONOMY 


ASTRONOMY  79 

its  center.  As  the  map  is  looked  at  on  the  page  this  is  the  lower 
left-hand  part.  When  this  is  turned  around,  so  it  is  up  and  the  map 
held  to  the  sky,  it  is  seen  at  once  that  the  Big  Dipper  is  above  the 
pole,  that  Cassiopeia  is  directly  below  the  pole,  that  Camelo- 
pardalus  is  to  the  west  of  the  pole,  and  that  Draco  is  to  the  east  of  it. 
In  a  similar  way  it  can  be  used  for  any  other  time  of  the  year  and 
of  the  night. 

The  other  maps  give  the  region  along  the  equator.  Consider 
the  time  May  21,  at  8  p.  M.  The  right  ascension  of  the  meridian, 
as  has  been  stated,  is  then  12  hours.  It  is  seen  by  referring  to  the 
right  ascension  marks,  which  are  on  the  center  line  of  these  maps, 
that  Map  III  must  be  used  in  this  case.  The  mark  XII  is  found 
on  this  map  where  the  ecliptic  crosses  the  equator  from  north  to 
south.  If  the  map  is  held  up  to  the  southern  sky,  so  that  this  point 
is  on  the  meridian  at  the  height  of  the  equator,  then  the  stars  will  be 
spread  out  relatively  on  the  map  the  same  as  they  are  on  the  sky. 
It  will  be  seen  then  that  Leo  is  a  little  west  of  the  meridian  and  a 
little  higher  than  the  equator.  On  the  meridian  south  of  the  equa- 
tor and  a  little  to  the  west  is  the  constellation  Crater.  On  the 
meridian  and  a  little  west  of  it,  running  across  the  equator,  is  the 
zodiacal  constellation  Virgo.  Five  hours  east  of  the  meridian  and 
30  degrees  south  of  it  is  the  constellation  Scorpio.  Consequently, 
on  this  date  and  at  this  time  of  day  Scorpio  should  be  seen  just  ris- 
ing in  the- southeastern  sky.  In  this  manner  these  maps  can  be  used 
for  any  day  in  the  year  and  any  time  of  the  day.  The  constellations 
and  the  maps  together  give  one  the  means  of  locating  any  group 
of  stars  he  wishes  at  any  time  whatever. 

Naming  the  Stars.  The  brightest  star  in  all  the  sky  is  called 
Sirius.  There  are  also  Vega,  Aldebaran,  Arcturus,  etc.  But  since 
the  number  of  stars  visible  to  the  unaided  eye  is  about  5,000  and 
the  number  within  the  reach  of  our  telescopes  runs  up  into  the  mil- 
lions, it  is  obvious  that  it  would  be  a  difficult  problem  to  have  names 
for  all  of  them.  As  a  matter  of  fact  only  a  relatively  small  number 
have  actually  been  given  names. 

One  of  the  methods  of  designating  the  stars,  besides  giving  them 
names,  is  by  stating  in  what  constellation  they  are  to  be  found 
and  their  rank  in  the  constellation  in  order  of  brightness.  The 
brightest  star  in  a  constellation  is  called  Alpha,  a  Greek  letter,  the 


80 


ASTRONOMY 


second,  Beta,  etc.  The  name  of  the  constellation  is  put  after  the 
Alpha,  Beta,  etc.,  in  the  genitive  case.  For  example,  according 
to  this  system  of  designating  the  stars  the  brightest  star  in  the  con- 
stellation Leo  is  called  Alpha  Leonis,  and  the  brightest  star  in  Cygnus 
(the  Swan)  is  called  Alpha  Cygni.  But  since  there  are  only  24 
letters  in  the  Greek  alphabet  it  is  obvious  that  this  method  has  its 
limitations.  After  the  Greek  letters  are  exhausted  the  Roman  letters 
are  sometimes  used.  But  the  list  of  Roman  letters  is  also  limited, 
and  in  a  constellation  having  thousands  of  stars  this  method  is 
obviously  entirely  inadequate. 

Another  method,  adopted  by  the  English  observer,  Flamsteed, 
about  1700,  is  to  number  all  the  stars  in  each  constellation  accord- 
ing to  their  right  ascension.  Thus  No.  1  in  Leo  would  be  that  star 
in  the^Lion  which  is  farthest  west;  that  is,  whose  right  ascension  is 
the  least.  The  objection  to  this  method  is  that  the  numbering  has 
no  relation  whatever  to  the  magnitudes  and  depends  upon  a  very 
arbitrary  and  irregular  division  of  the  whole  sky  into  constella- 
tions. If,  after  a  catalogue  is  made,  new  stars  should  be  added,  it 
would  be  necessary  to  re-number  all  of  those  which  had  a  greater 
right  ascension. 

Still  another  method  of  designating  the  stars  is  to  give  their  num- 
ber in  a  certain  catalogue  irrespective  of  the  constellation  in  which 
they  appear.  The  stars  in  these  catalogues  are  often  arranged  and 
numbered  in  the  order  of  their  right  ascension.  While  this  system 
has  no  relation  to  their  magnitudes,  it  depends  upon  their  positions 
in  the  sky  and  is  convenient  when  one  wishes  to  make  an  observing 
program.  If  a  certain  star  will  be  visible  on  a  certain  evening  at  a 
convenient  time  for  observation,  then  all  of  those  whose  numbers  are 
near  it  will  also  be  visible  at  the  same  time.  The  fact  that  they  are 
north  or  south  of  it  makes  no  important  difference  unless,  indeed, 
they  are  so  far  south  as  to  be  always  invisible. 

Star  Catalogues.  The  earliest  star  catalogue  of  which  we  have 
any  record  is  a  catalogue  of  1,080  stars  made  by  Hipparchus  for  the 
epoch  125  B.  c.  It  was  inspired  by  the  appearance  of  what  is  called 
a  temporary  star.  In  a  region  of  the  sky  in  which  no  star  had  before 
that  time  been  visible  a  brilliant  star  suddenly  blazed  out  and  after 
a  few  months  disappeared.  Hipparchus  was  astonished  by  the 
phenomenon  since  nearly  all  the  stars  are  always  the  same.  He 


ASTRONOMY 


81 


determined  then  to  make  a  catalogue  of  all  the  brightest  stars, 
giving  their  positions  in  order  that  later  astronomers  might  be  able 
to  determine  whether  they  were  appearing  and  disappearing  and 
whether  they  were  changing  their  positions  in  the  sky.  This  cata- 
logue of  Hipparchus  was  revised  and  reduced  to  the  epoch  150  A.D. 
by  the  astronomer  Ptolemy. 


Fig.  35.     Photograph  of  a  Part  of  the  Constellation  Taurus  Showing  the  Hyades  near 
the  Top  of  the  Picture 

Tycho  Brahe,  who  has  been  mentioned  as  being  a  great  observer, 
in  1580  made  a  catalogue  of  1,015  stars.  Since  that  time  star  cata- 
logues have  been  very  numerous. 

One  of  the  greatest  made  by  direct  telescopic  observations  is 
that  of  Argelander  (1799-1875)  which  contains  324,198  stars.  While 
only  about  5,000  stars  are  visible  to  the  unaided  eye,  Argelander 


82  ASTRONOMY 

made  his  catalogue  with  a  telescope  2.5  inches  in  diameter.  There 
are  many  catalogues  containing  from  a  few  hundred  to  a  few  thousand 
stars  whose  positions  are  given  with  the  very  highest  degree  of 
precision.  They  are  useful  in  determining  with  great  accuracy  the 
positions  of  the  heavenly  bodies  which  move,  such  as  the  planets 
and  comets;  for  it  is  only  necessary  to  locate  a  wandering  body 
with  respect  to  the  known  fixed  stars  in  order  to  have  its 
position. 

Recently  an  enormous  catalogue  made  by  another  plan  has  been 
projected  and  nearly  completed.  It  was  found  in  1882  that  the  stars 
could  be  photographed.  This  suggested  to  the  English  astronomer 
Gill  the  making  of  a  catalogue  of  the  whole  sky  by  the  photographic 
process.  A  photograph  of  a  region  is  taken  and  on  the  photographic 
plate  there  will  be  the  images  of  some  stars  whose  positions  are 
already  known.  When  the  distances  and  directions  of  the  unknown 
stars  from  the  known  stars  are  measured,  their  positions  become 
known.  The  work  of  making  this  great  catalogue  was  undertaken 
by  international  co-operation  and  the  work  was  divided  among  many 
observatories.  Necessarily  some  photographs  had  to  be  taken  from 
points  on  the  earth  north  of  its  equator  and  others  from  places  south 
of  its  equator.  Each  plate  covers  about  four  square  degrees  of  sky, 
and  since  they  must  overlap  in  order  to  connect  with  one  another, 
and  since  it  is  advisable  to  have  the  whole  sky  covered  twice,  nearly 
22,000  plates  are  required.  On  these  plates  about  15,000,000  of  stars 
will  be  shown.  Many  of  them  will  be  very  faint  and  it  is  at  present 
planned  to  measure  and  catalogue  only  1,500,000  of  them.  Fig.  35 
is  a  photograph  of  a  region  in  the  constellation  Taurus  and  includes 
the  stars  known  as  the  Hyades,  which  can  be  seen  as  a  little  cluster 
near  the  top  of  the  picture. 

Magnitudes  of  Stars.  The  quantity  of  light  we  receive  from 
the  different  stars  differs  greatly,  and  probably  we  do  not  get  precisely 
the  same  light  in  quantity  .and  quality  from  any  two  stars.  The 
magnitude  of  a  star  refers  to  the  quantity  of  light  we  receive  from 
it  and  has  no  necessary  relation  to  its  actual  size  or  brilliance.  A 
rather  faint  star  near  us  would  give  us  more  light  than  a  much  larger 
one  farther  away.  The  stars  which  can  be  seen  without  the  aid  of  a 
telescope  are  divided  arbitrarily  into  six  groups.  The  20  brightest 
stars  constitute  the  first  group,  and  the  average  of  the  20  brightest  is 


ASTRONOMY  83 

the  ideal  first-magnitude  star.  The  faintest  stars  that  can  be  seen 
without  a  telescope  are  the  sixth-magnitude  group. 

It  is  found  by  observations  that  a  first-magnitude  star  gives  us 
100  times  as  much  light  as  a  sixth-magnitude  star.  Of  course,  what 
is  a  sixth-magnitude  star  depends  somewhat  upon  the  sensitiveness 
of  the  eye  of  the  observer  if  it  is  defined  as  the  faintest  star  which 
can  be  seen  without  a  telescope.  It  also  depends  upon  various  other 
factors,  such  as  the  transparency  of  the  atmosphere  and  the  presence 
or  absence  of  moonlight  or  artificial  light.  But  those  stars  which  are 
OFTF  as  bright  as  the  ideal  first-magnitude  star  are  at  least  near  the 
limits  of  visibility  under  ordinary  conditions,  and  are  taken  as  the 
stars  of  the  sixth  magnitude.  If  the  ratio  of  light  of  the  first-magni- 
tude star  to  the  sixth-magnitude  star  is  as  100  to  one,  it  is  found  in 
order  that  the  ratios  from  the  first  to  the  second,  the  second  to  the 
third,  and  so  on,  shall  all  be  equal,  that  the  ratio  of  the  light  from  a 
first-magnitude  star  to  that  from  a  second-magnitude  star  is  as  2.512 
to  1;  and,  in  general,  the  ratio  of  the  light  received  from  any  star 
to  one  in  the  next  group  fainter  is  this  same  number. 

The  stars  next  fainter  than  those  which  are  visible  without  a 
telescope  constitute  the  seventh-magnitude  group.  Then  follow  the 
eighth,  ninth,  and  so  on.  The  faintest  stars  which  are  in  reach  of 
our  best  modern  instruments  are  of  about  the  seventeenth  mag- 
nitude. 

If  a  star  is  brighter  than  the  ideal  first-magnitude  star  its  magni- 
tude is  taken  as  less  than  one.  For  example,  the  star  Vega,  being 
brighter  than  the  ideal  first-magnitude  star,  has  a  magnitude  0.2; 
and  the  brightest  star  in  the  sky,  Sirius,  has  a  magnitude  — 1.4.  In 
describing  the  magnitudes  of  the  stars  it  is  necessary  to  use  decimals 
in  order  to  attain  a  considerable  degree  of  accuracy  because  the  stars 
do  not  fall  into  the  ideal  groups.  There  are  many  between  the  exact 
first  and  the  exact  second  magnitudes,  and  so  on,  for  all  other  even 
magnitudes.  The- star  Vega  is  brighter  than  the  first-magnitude  star 
but  not  a  full  magnitude  brighter.  Consequently,  its  magnitude  is 
not  0.0,  which  would  be  a  full  magnitude  brighter,  but  0.2.  The 
star  Sirius  is  more  than  one  magnitude  brighter  than  Vega  and  going 
beyond  the  0.0  has  to  be  represented  by  a  negative  number.  It  is 
2.4  magnitudes  brighter  than  the  ideal  first-magnitude  star.  On  this 
basis  the  magnitude  of  the  sun  is  approximately  —26. 


84 


ASTRONOMY 


TABLE  II 
List  of  First=Magnitude  Stars 


Star 

Magni- 
tude 

Right 
Ascension 

Declination 

Color 

When    on 
Meridian 
at  8  P.  M. 

Sirius 

-1.4 

6hr.40  m. 

-16°  34' 

Bluish  white 

July       1 

(Greater  Dog) 

Arcturus 

0.0 

14        10 

+  19   48 

Orange 

Oct.     24 

(Bootes) 

Vega 

0.2 

18       33 

+38   40 

Pale  blue 

Jan.       1 

(Lyra) 

Capella 

0.2 

5         8 

+45   52 

Yellowish 

June      6 

(Auriga) 

Rigel 

0.3 

5         9 

-  8   20 

White 

June      6 

(Orion) 

Canopus 

0.4 

6       21 

-52   38 

Bluish 

June    26 

(Argo) 

Procyon 

0.5 

7      33 

+  5   32 

White 

July     12 

(Smaller  Dog) 

Betelgeuse 

0.9 

5      49 

+  7   23 

Ruddy 

June    17 

(Orion) 

Alpha  Centauri 

1.0 

14      31 

-60   20 

White 

Oct.      28 

Achernar 

1.0 

1       33 

-57    51 

White 

April    11 

(Eridanus) 

Altair 

1.0 

19      45 

+  8   33 

Yellowish 

Jan.      17 

(Aquila) 

Aldebaran 

1.0 

4      30 

+  16    16 

Red 

May    28 

(Taurus) 

An  tares 

1.1 

16      22 

-26    10 

Deep  red 

Nov.    27 

(Scorpio) 

Pollux 

1.1 

7       38 

+28    19 

Orange 

July     15 

(Gemini) 

Spica 

1.2 

13       19 

-10   32 

White 

Oct.      11 

(Virgo) 

Beta  Centauri 

1.2 

13       55 

-59   48 

White 

Oct.     20 

Alpha  Crucis 

1.3 

12       20 

-62   26 

Bluish  white 

Sept.    26 

Fomalhaut 

1.3 

22       52 

-30    16 

Ruddy 

March  5 

(Piscis  Australis) 

Regulus 

1.4 

10         2 

+  12   33 

White 

Aug.     21 

(Leo) 

Deneb 

1.4 

20       38 

+44   53 

White 

Feb.       1 

(Cygnus) 

It  is  easy  to  get  a  general  idea  of  the  relative  brightness  of  stars 
separated  by  any  magnitude.  Suppose,  for  example,  we  wish  to  find 
how  much  brighter  stars  of  the  first  magnitude  are  than  those  of  the 
seventeenth.  As  has  been  stated,  stars  of  the  first  magnitude  are 
100  times  brighter  than  those  of  the  sixth;  similarly,  those  of  the 
sixth  magnitude  are  100  times  brighter  than  those  of  the  eleventh. 
Therefore,  the  stars  of  the  first  magnitude  are  1002=  10,000  times 
brighter  than  those  of  the  eleventh.  Those  of  the  eleventh  magnitude 
are  100  times  brighter  than  those  of  the  sixteenth.  Consequently, 
the  stars  of  the  first  magnitude  are  10,000X100=1,000,000  times 
brighter  than  those  of  the  sixteenth  magnitude.  Those  of  the  sixteenth 


ASTRONOMY 


85 


TABLE  III 
Number  of  Stars  Visible  to  Naked  Eye 


First  magnitude 20 

Second  magnitude 65 

Third  magnitude 190 


Fourth  magnitude 425 

Fifth  magnitude 1100 

Sixth  magnitude 3200 


magnitude  are  2.5  times  brighter  than  those  of  the  seventeenth. 
Therefore,  we  have  for  the  final  result  that  stars  of  the  first  magni- 
tude are  2,500,000  times  brighter  than  those  of  the  seventeenth. 
Those  of  the  sixth  magnitude  are  25,000  times  brighter  than  those  of 
the  seventeenth.  These  results  give  an  idea  of  the  relative  power  of 
our  modern  instruments  compared  to  that  of  the  unaided  eye. 
Computing  the  relative  brightness  of  the  sun  in  the  same  way,  we 
find,  under  the  hypothesis  that  its  magnitude  is  -  26,  that  it  is  in 
round  numbers  60,000,000,000  times  brighter  than  the  ideal  first- 
magnitude  star. 

First=Magnitude  Stars.  The  twenty  stars  that  constitute  the 
first-magnitude  group  are  conspicuous  objects  in  the  heavens  which 
always  keep  their  positions  relative  to  the  others.  They  serve  as 
guideposts  for  a  study  of  the  constellations,  and  those  which  are 
visible  in  the  latitude  of  the  observer  should  be  familiar  to  him. 
They  are  distinguishable  by  their  brightness,  their  color,  and  their 
relations  to  fainter  stars  near  them.  A  table  of  the  first-magnitude 
stars  is  given  herewith,  including  also  in  the  second  column  their 
magnitudes;  in  the  third,  their  right  ascensions;  in  the  fourth,  their 
declinations;  in  the  fifth,  their  colors;  and  in  the  sixth,  the  times  of 
year  at  which  they  cross  the  meridian  at  8  P.M.  The  names  of  the 
constellations  to  which  the  stars  belong  are  given  in  parenthesis 
under  their  proper  names,  except  in  those  cases  where  the  stars  have 
no  special  names.  From  the  principles  which  have  been  explained 
above,  it  is  a  relatively  simple  matter  to  find  their  approximate 
positions  in  the  sky  at  any  time  and,  by  means  of  Table  II,  to 
locate  them.  When  they  have  once  been  located  and  carefully 
observed  for  their  own  peculiarities  and  relations  to  neighboring 
stars,  they  will  not  be  forgotten. 

Number  of  Stars.  It  is  a  common  impression  that  the  stars 
which  are  visible  to  the  unaided  eye  are  absolutely  numberless,  and 
they  are  often  compared  to  the  grains  of  sand  on  the  seashore.  As 


Fig.  36.     Star  Cloud  in  Sagittarius  Photographed  by  Barnard 


ASTRONOMY  87 

a  matter  of  fact,  they  are  not  only  finite  in  number,  but  their  number 
is  not  very  great.  In  Table  III  is  given  the  number  of  stars  in  the 
whole  sky  in  the  first  six  magnitudes. 

It  is  seen  that  the  whole  number  of  stars  in  all  the  sky  visible 
without  telescope  is  5,000.  At  any  one  time  fewer  than  half  of  these 
are  visible  because  only  one-half  of  the  sky  is  above  the  horizon,  and 
those  faint  stars  whose  light  must  come  through  the  denser  atmos- 
phere near  the  horizon  are  not  visible. 

It  will  be  noticed  from  Table  III  that  each  fainter  magnitude 
has  approximately  three  times  as  many  stars  as  the  preceding  one. 
If  this  ratio  continues  it  is  found  by  calculation  that  there  are  about 
200,000  stars  in  the  first  nine  magnitudes,  and  the  actual  observa- 
tions are  in  harmony  with  this  computation.  If  the  ratio  kept  up 
indefinitely  there  would  be  infinitely  many  stars.  But  beyond  the 
ninth  magnitude  it  begins  to  fall  off,  so  that  each  fainter  group  has 
fewer  than  three  times  as  many  stars  in  it  as  are  in  the  preceding 
group.  It  is  not  known  with  any  high  degree  of  accuracy  how  many 
stars  there  are  in  the  first  17  magnitudes,  which  are  within  the  range 
of  the  most  powerful  telescopes,  but  from  counts  of  many  representa- 
tive regions  it  is  concluded  that  there  are  probably  more  than 
100,000,000  of  them.  Fig.  36  is  a  photograph  of  a  portion  of  a 
part  of  the  great  star  cloud  in  Sagittarius.  This  bright  part  of  the 
Milky  Way  is  in  the  southern  sky  in  the  early  evening  in  mid-summer. 

Proper  Motions  of  Stars.  The  stars  are  called  "fixed,"  and 
the  fainter  ones  are  the  most  nearly  fixed  of  anything  we  know. 
Yet  they  are  not  absolutely  fixed.  They  move  slowly  with  respect 
to  one  another,  and  with  accurate  instruments  it  is  possible  in  many 
cases  to  detect  these  changes  in  a  relatively  short  time.  The.  nipt  ion  s 
ojjjie  stars  relatively  to  one  another,  or  rather  their  motions  with 
respect  to  the  ideal,  fixed  right_a^ejisipjijin^  are 

called  their  proper  motions.  The  greatest  proper  motion  known  is 
only  8.7  seconds  per  year.  Most  of  the  stars  move  less  than  one 
second  per  century.  The  smallness  of  this  greatest  motion  of  8.7 
seconds  per  year  is  illustrated  by  the  fact  that  it  would  take  this 
star  220  years  to  travel  over  an  arc  equal  to  the  apparent  diameter 
of  the  moon.  This  star  is  of  the  eighth  magnitude  and  is  therefore 
invisible  to  the  unaided  eye.  -  The  proper  motions  of  all  visible  stars 
are  so  small  that  the  sky  appears  to  us  almost  as  it  did  to  the  ancient 


88  ASTRONOMY 

Babylonians  who  first  named  the  constellations.  They  looked  up 
into  the  night  sky  and  saw  the  Big  Dipper,  the  Pleiades,  Orion,  etc., 
shining  with  almost  the  same  luster  as  that  with  which  these  splendid 
stars  shine  at  the  present  time,  and  situated  relatively  to  one  another 
sensibly  as  they  are  now. 

The  proper  motions  of  the  stars  are,  of  course,  due  to  their 
actual  motions.  The  sun,  being  a  star  also,  has  an  actual  motion 
through  space.  It  is  moving  nearly  toward  the  star  Vega  at  the  rate 
of  400,000,000  miles  per  year,  or  at  the  rate  of  12  miles  per  second. 
The  motions  of  the  stars  toward  us  or  from  us  are  determined  by 
means  of  the  spectroscope.  It  is  found  from  those  which  so  far  have 
been  observed  by  means  of  the  spectroscope  (only  those  of  the  eighth 
magnitude  or  brighter),  that  on  the  average  they  move  at  the  rate 
of  about  20  miles  per  second,  or  about  700,000,000  miles  per  year. 
One  might  imagine  at  first  thought  that,  if  a  star  were  coming  toward 
us  at  the  rate  of  700,000,000  miles  per  year,  or  at  the  much  greater 
rate  at  which  some  of  the  stars  move,  it  would  speedily  become 
brighter,  and  that  if  it  were  receding,  it  would  diminish  in  brilliance. 
The  fact  is,  however,  that  their  distances  are  so  great  that  these 
changes  do  not  alter  their  apparent  magnitudes  by  sensible  quan- 
tities in  the  course  of  the  few  centuries  or,  at  the  most,  the  few 
thousand  years,  they  have  been  under  observation. 

The  Milky  Way  or  Galaxy.  There  is  a  band  of  hazy  light, 
averaging  about  20  degrees  in  width,  stretching  around  the  sky  in 
approximately  a  great  circle.  A  keen  eye,  under  good  circumstances, 
can  see  that  it  is  made  up,  at  least  in  its  coarser  parts,  of  fine  stars, 
and  it  was  commonly  supposed  by  the  ancient  Greeks  that  it  was  a 
vast  aggregation  of  stars  so  minute  that  they  were  not  individually 
distinguishable.  The  Pawnee  Indians  of  our  western  plains  have 
the  curious  story  that  it  is  a  cloud  of  dust  made  by  a  buffalo  and 
horse  racing  across  the  sky.  For  a  long  distance  it  presents  a  length 
wise  division.  They  thought  the  horse  ran  on  one  side,  where  th 
stars  are  a  little  larger,  and  kicked  up  a  coarse  dust;  and  that  th 
buffalo  ran  on  the  other  side  and  kicked  up  a  fine  dust,  which  con- 
stitutes the  part  whose  individual  stars  are  beyond  visibility. 

The  Milky  Way  runs  diagonally  across  the  sky;  that  is,  it  d 
not  follow  an  hour  circle  or  a  declination  circle.     It  crosses  the 
equator  at  points  whose  right  ascensions  are  about  7  hours  and  19 


Fig.  37. 


Dark  Lanes"  in  the  Star  Clouds  in  Ophiuchus,  Photographed  by  Barnard  at 
the  Yerkes  Observatory 


90  ASTRONOMY 

hours,  and  its  inclination  to  the  equator  is  about  63  degrees.  The 
north  pole  of  the  Galaxy  has  a  right  ascension  of  about  13  hours 
and  a  declination  of  27  degrees.  It  is  extremely  irregular  in  outline, 
having  many  dense  star  clouds  and  at  other  places  dark  holes  and 
dark  rifts  across  it.  Fig.  37  is  a  photograph  of  a  portion  of  the  Milky 
Way  in  Ophiuchus,  showing  star  clouds,  nebulas,  and  dark  lanes. 

How  to  Find  the  Pole  Star.  The  most  conspicuous  group  of 
stars  in  the  northern  heavens  which  is  always  visible  to  observers  of 
our  latitude,  is  the  Great  Dipper.  Everyone  who  knows  any  stars  at 
all  is  familiar  with  this  group.  Its  outline  is  perfectly  definite  and  is 
made  up  of  seven  stars  of  about  equal  magnitude — the  second. 
When  the  Dipper  has  been  located  it  is  easy  to  find  the  pole  star. 
Start  at  the  bottom  of  the  bowl  of  the  Dipper  on  the  side  opposite 
the  handle,  go  along  the  edge  of  the  Dipper  opposite  the  side  of  the 
handle  and  continue  about  five  times  the  distance  between  these 
two  stars,  and  the  pole  star  is  reached.  The  two  stars  in  the  Dipper 
in  the  side  opposite  the  handle  are  called  the  "Pointers,"  for  they 
are  almost  exactly  in  a  line  with  the  pole  star.  Knowing  this  fact 
and  the  distance  of  the  pole  star  from  them  compared  to  their  dis- 
tance apart,  it  is  always  easy  to  locate  it.  It  is  near  no  other  bright 
star  and  is  itself  of  the  second  magnitude.  Since  it  is  always  visible  in 
the  northern  hemisphere  it  serves  as  a  unit  for  determining  the  magni- 
tudes of  stars  whose  brightness  is  approximately  equal  to  that  of  itself. 

In  describing  the  positions  of  stars  it  is  extremely  convenient 
to  say  that  one  is  in  a  certain  direction  and  distant  a  certain  number 
of  degrees  from  a  known  star.  Ordinarily,  a  person  has  a  vague 
idea  of  the  distance  covered  by  20  degrees  on  the  sky,  for  he  knows  the 
whole  circumference  is  divided  into  360  degrees.  Therefore,  it  is 
useful  to  have  in  mind  a  number  of  distances  between  stars  for  use 
as  units.  One  convenient  unit  is  the  altitude  of  the  pole  star  above 
the  horizon.  It  was  shown  above  that  it  is  equal  to  the  latitude  of 
the  observer.  Consequently,  if  the  observer's  latitude  were  40 
degrees  the  altitude  of  the  pole  star  would  be  40  degrees.  This  gives 
a  means  of  estimating  distances  of  about  40  degrees.  An  error  is 
likely  to  creep  in  because  the  distance  from  the  horizon  in  a  ver- 
tical direction  from  the  pole  star  generally  seems  somewhat  different 
from  a  distance  of  40  degrees  between  two  stars  which  are  not  on  a 
vertical  circle.  The  distance  between  the  Pointers  in  the  Big  Dipper 


ASTRONOMY  91 

is  approximately  five  degrees.  This  serves  as  a  very  convenient 
unit  for  measuring  the  small  distances.  The  distance  between  the 
stars  at  the  bottom  of  the  Big  Dipper  is  seven  degrees.  And  the 
distance  from  the  Pointer  nearest  the  pole  to  the  pole  star  is  28  degrees. 

Fig.  38  gives  an  outline  map  of  the  Big  Dipper  and  the  pole  star 
with  the  names  of  the  stars.  In  this  case  the  scheme  of  naming  the 
brightest  star  in  the  constellation  Alpha,  the  next  brightest  Beta, 
and  so  on,  is  not  followed.  The  star  Zeta  at  the  bend  in  the  handle 
of  the  Big  Dipper,  which  was  called  Mizar  by  the  Arabs,  has  a  very 
faint  star  near  it  called  Alcor,  which  means  "the  test."  The  Arabs 
considered  the  eyes  of  a  person  good  if  he  could  see  this  faint  test 
star.  The  difficulties  of  seeing  it  are  due 
to  the  fact  that  it  is  near  the  bright  star 
Mizar  and  is  itself  faint.  This  star  should 
be  looked  for  and  it  will  be  found  that 
every  one  can  easily  see  it  whose  eyes  are 
considered  anywhere  near  normal. 

The  star  Alcor  is  of  the  fifth  mag- 
nitude and   its   distance  from  Mizar  is 

11.5  minutes  of   arc.     The  shortest  dis- 
tance between  two  stars  which  are  visi- 
ble as  distinct  objects  without  telescopic 

aid,  is  about  three  minutes.    With  a  tel-      Fig.  38.    The  Big  Dipper  and 

the  Pole  Star 

escope  it  is  found  that  Mizar  itself  is  a 

fine    double,  composed    of    a  white  star  and   one   of   an   emerald 

color.    The  distance  of  the  two  components  from  each  other  is  about 

14.6  seconds  of  arc,  and  a  3-inch  telescope  will  easily  show  them. 
It  is  not  to  be  inferred  that  the  two  suns  which  compose  this  system 
are  really  very  close  together  because  they  appear  close  together. 
This  apparent  nearness  is  the  consequence  of  their  vast  distance  from 
us.     It  is  not  known  just  how  far  they  are,  away  but  almost  cer- 
tainly it  takes  their  light  more  than  100  years  to  come  to  us.  The 
meaning  of  this  statement  becomes  apparent  when  one  remembers 
that  light  travels  at  the  rate  of  186,330  miles  per  second. 

The  brighter  component  of  Mizar  was  found  to  be  a  double  by 
the  use  of  the  spectroscope  in  1889.  This  discovery  by  Professor  E.  C. 
Pickering  was  the  first  of  its  kind.  A  spectroscopic  binary  is  one  in 
which  the  two  components  are  so  close  and  their  distance  from  us 


92  ASTRONOMY 

so  great  that  they  are  not  visible  as  separate  objects  with  any  tele- 
scope. But  by  an  adaptation  of  the  spectroscope,  whose  description 
will  be  deferred,  it  is  possible  under  certain  circumstances  to  deter- 
mine their  binary  character.  Not  only  this,  but  in  the  case  of  the 
spectroscopic  binaries  it  is  possible  to  find  out  other  things  about 
the  system,  particularly  the  actual  distance  of  the  stars  apart  and 
their  combined  mass.  In  the  case  of  the  brighter  component  of  Mizar 
the  stars  perform  a  revolution  about  their  center  of  gravity  in  20.5 
days  and  are  at  a  distance  of  25,000,000  miles  from  each  other.  Their 
combined  mass  is  about  five  times  that  of  our  sun. 

The  pole  star  is  also  an  object  of  much  interest.    It  is  found  to 
be  a  double  star  having  a  faint  companion  of  the  ninth  magnitude 
at  a  distance  from  it  of  about  18.5  seconds.    The  component  can  be 
seen  with  a  5-inch  telescope  using  a  magnifying  power  of  from  75 
to  100  diameters.    The  larger  one  of  the  two  components  was  foum 
in  1899  to  be  a  spectroscopic  binary.    This  group  of  stars  is  so  h 
from  us  that  40  years  are  required  for  its  light  to  come  to  us;  t] 
is,  we  see  it  as  it  was  40  years  ago. 

Cassiopeia.   The  right  ascension  of  this  constellation  is  about  zei 
hours.     Consequently,  it  is  on  the  meridian  at  8  p.  M.  November  21 
But  if  one  wishes  to  find  it  without  referring  to  its  right  ascensi< 
and  declination  it  can  be  located  by  going  from  the  Great  Dip] 
through  the  North  Star  and  as  far  beyond  as  that  distance.    It 
therefore,  above  the  pole  when  the  Dipper  is  directly  below. 
siopeia  is  distinguished  by  a  zigzag,  or  letter  W,  composed  of  stai 
from  the  second  to  the  fourth  magnitude.    The  brightest  star  is  at 
the  bottom  of  the  second  part  of  the  W.    This  is  found  to  be  a  fine 
double  star  whose  colors  are  rose  and  blue,  and  it  can  be,  seen  sepa- 
rately with  a  2-inch  telescope. 

One  of  the  most  interesting  objects  in  the  constellation  of 
Cassiopeia  is  the  star  Eta,  which  is  near  the  middle  of  the  third  stroke 
of  the  W,  and  about  two  degrees  from  the  brightest  star.  It  is  a  fine 
double  star  and  can  be  separated  with  a  3-inch  telescope.  These 
two  stars  form  a  physical  system  and  revolve  around  their  center  of 
gravity  in  a  period  of  about  200  years.  They  are  so  far  away  that 
it  takes  their  light  about  nine  years  to  come  to  us. 

In  the  constellation  Cassiopeia  a  temporary  star  suddenly 
appeared  in  1572.  Its  dazzling  splendor  and  the  fact  that  it  had 


ASTRONOMY  93 

recently  appeared,  attracted  the  attention  of  Tycho  Brahe  who  was 
then  a  young  man,  and  turned  his  attention  to  astronomy. 

The  Equinoxes.  It  is  possible  to  find  the  positions  of  the 
equinoxes  by  means  of  the  processes  described  above,  but  it  is  also 
possible  to  locate  them  easily  by  direct  observations  of  the  stars. 

To  find  the  vernal  equinox,  draw  a  line  from  Polaris  through  the 
most  westerly  star  in  the  W  of  Cassiopeia  and  prolong  it  90  degrees. 
The  point  where  it  strikes  the  equator  is  the  vernal  equinox.  The 
autumnal  equinox  is  obtained  by  drawing  a  line  from  Polaris  through 
Delta  Ursae  Majoris  and  prolonging  it  until  it  strikes  the  equator. 
This  point  is  in  the  constellation  Virgo  about  10  degrees  north  and 
20  degrees  west  of  the  first-magnitude  star  Spica. 

Lyra.  Lyra  (the  Lyre)  is  a  small  constellation  but  one  of  the 
most  interesting  of  them  all.  Its  mean  right  ascension  is  about  18.7 
hours  and  its  declination  is  about  +40  degrees.  It  is  conspicuous 
because  of  the  brilliant  first-magnitude  star  Vega  which  is  in  it. 

It  was  explained  in  connection  with  the  discussion  of  the  pre- 
cession of  the  equinoxes,  that  the  plane  of  the  earth's  equator  slowly 
shifts  on  account  of  the  attraction  of  the  moon  and  sun  on  the  earth's 
equatorial  bulge.  This  causes  the  axis  of  the  earth  to  point  con- 
tinually in  different  directions.  The  pole  of  the  sky  is  the  point  on 
the  celestial  sphere  toward  which  the  axis  of  the  earth  is  directed. 
On  account  of  the  precession  of  the  equinoxes  the  position  of  the  pole 
of  the  sky  is  continually  changing.  It  describes  a  circle  whose  radius, 
is  23.5  degrees  and  whose  center  is  the  pole  of  the  ecliptic,  in  a  period 
of  26,000  years.  It  happens  that  this  circle  which  the  celestial  pole 
describes  passes  very  near  the  star  Vega.  In  12,000  years  from  now 
the  pole  will  be  very  near  Vega  and  at  this  time  that  star  will  be  the 
pole  star.  How  much  more  glorious  and  conspicuous  an  object  it 
will  be  than  Polaris! 

Lyra  is  also  a  constellation  of  interest  because  it  is  nearly  in 
that  direction  that  the  sun  with  its  planets  is  moving. 

There  are  two  stars  of  the  fourth  magnitude,  Epsilon  and  Zeta 
Lyrae,  each  about  two  degrees  from  Vega.  One  is  northeast  and  the 
other  southeast,  and  with  Vega  they  form  a  nearly  equilateral 
triangle.  The  star  Epsilon  is  a  close  double,  composed  of  two  nearly 
equal  stars  separated  by  a  distance  of  207  seconds  of  arc.  It  is  a 
famous  test  object  for  observation  without  optical  aid.  A  person 


94 


ASTRONOMY 


with  good  eyes  and  under  favorable  atmospheric  conditions  in  tl 
absence  of  sky  illumination  can  see  the  two  components  as  separat 
objects.    It  is  worthy  of  note  that  it  never  was  known  to  be  a  double, 
so  far  as  the  records  show,  until  after  the  invention  of  the  telescope. 
If  it  is  beyond  the  visibility  of  an  observer  he  can  usually  see  it  wil 
the  aid  of  opera  glasses.    The  object  does  not  lose  its  interest  wh( 


Fig.  39.     The  Ring  Nebula  in  Lyra 

viewed  through  a  telescope.  When  examined  under  considerable 
optical  power  the  two  components,  which  are  on  the  limits  of  visi- 
bility with  the  unaided  eye,  are  seen  to  be  very  far  apart,  and  each 
one  of  them  is  found  itself  to  be  a  double.  Thus,  that  which,  at 
least  at  first  glance,  seems  to  be  a  single  faint  star  in  the  sky,  when 
examined  with  a  powerful  instrument,  turns  out  to  be  a  system  of 
four  magnificent  suns. 


ASTRONOMY 


95 


Another  interesting  object  in  this  constellation  is  the  ring 
nebula.  (See  Fig.  39.) 

Scorpio.  Scorpio  (the  Scorpion)  is  the  ninth  zodiacal  constella- 
tion and  the  most  brilliant  of  all.  In  fact,  it  is  one  of  the  finest 
southern  constellations  that  can  be  seen  in  our  latitude.  It  is  always 
easily  recognized  by  the  fiery  red  first-magnitude  star  Antares  which 


Fig.  40.     The  Great  Star  Cluster  in  Scorpio 

in  light-giving  power  is  equal  to  900  suns  such  as  our  own.  About 
five  degrees  northwest  of  Antares  is  a  very  compact  and  fine  cluster 
of  stars  in  which  about  5,000  of  these  objects  are  crowded  in  a 
region  apparently  one-fifth  the  size  of  the  moon.  (See  Fig.  40.) 

Bootes.  Bootes  (the  Hunter)  is  a  large  constellation  reaching 
from  near  the  equator  to  within  35  degrees  of  the  pole,  and  having 
a  mean  right  ascension  of  about  15  hours.  The  most  conspicuous 


96  ASTRONOMY 

object  in  it  is  the  brilliant  orange-colored,  first  magnitude  star  Arc- 
turus.  This  star  is  approaching  us  at  the  rate  of  about  five  miles  a 
second,  but  it  is  so  far  away  that  it  takes  its  light  100  years  to  come 
to  us.  Its  light-giving  power  is  about  1,300  times  that  of  our  sun. 

Leo.  Leo  (the  Lion)  is  another  one  of  the  zodiacal  constellations 
and  the  ecliptic  passes  very  near  to  its  brightest  star,  Regulus.  It 
is  about  60  degrees  west  of  Arcturus  and  is  easily  recognized  by  a 
sickle  of  seven  stars  opening  to  the  southwest,  with  Regulus  at  the 


Fig.  41.     Photograph  or  the  Pleiades — the  "Seven  Sisters" — Made  at  the  Yerkes  Observatory 

end  of  its  handle.  One  of  the  many  things  of  interest  in  connection 
with  this  constellation  is  that  the  November  meteors  seem  to  radiate 
from  it. 

Taurus.  Taurus  (the  Bull)  contains  the  Pleiades,  the  Hyades, 
and  Aldebaran.  The  Pleiades  include  seven  fourth-magnitude  stars 
forming  roughly  a  small  dipper,  and  are  mentioned  in  the  sacred 
writings  and  the  folk-lore  stories  of  primitive  peoples  more  often 
than  any  other  group  of  stars  in  the  sky.  The  ancient  Greeks  called 
them  the  "seven  sisters' '  and  had  a  story  of  how  one  was  later  lost. 
Apparently,  those  who  wrote  about  them  at  that  date  were  able  to 
see  only  six.  Now  seven  are  easily  visible  to  anyone  of  good  eyesight 
under  favorable  conditions,  and  to  those  with  more  acute  vision, 
under  the  best  circumstances,  ten  or  eleven  are  visible. 


ASTRONOMY  97- 

In  Fig.  41  is  given  a  photograph  of  the  Pleiades  together  with 
many  stars  which  can  be  seen  only  with  optical  aid.  While  the 
Pleiades  appear  to  be  small  insignificant  objects  in  the  heavens  they 
are,  as  a  matter  of  fact,  giant  suns.  Those  brighter  ones  which  can 
be  seen  without  a  telescope  are  from  200  to  300  times  as  great  in 
light-giving  power  as  our  own  sun.  They  are  so  far  away  that, 
according  to  the  discussion  of  Newcomb,  it  takes  their  light  267 
years  to  come  to  us.  At  one  time  a  German  astronomer,  Maedler, 
supposed  that  Alcyone,  the  brightest  star  of  this  group,  was  in  the 
center  of  the  universe.  This  idea  has  been  abandoned  as  there  is  no 
evidence  whatever  to  support  it.  The  ecliptic  passes  about  four 
degrees  south  of  the  Pleiades.  Consequently,  the  sun,  moon,  and 
planets  pass  near  it,  and  in  fact  the  moon  sometimes  eclipses  these 
stars. 

The  Hyades  are  a  large  and  diffuse  group  of  stars  which  have 
been  found  by  recent  observations  of  Boss  to  be  moving  with  about 
equal  speed  towaid  a  distant  point  in  the  sky.  This,  of  course,  does 
not  necessarily  mean  that  they  are  going  td  collide  in  the  remote 
future.  But  the  parallelism  of  their  motion  and  the  equality  of 
their  speed  shows  that  beyond  question  they  have  had  a  common 
origin.  The  examinations  of  them  with  the  spectroscope,  which  is 
an  instrument  that  enables  us  to  determine  the  chemical  constitution 
of  luminous  bodies,  shows  that  these  stars  are  very  much  alike  in 
their  constitution,  a  fact  which  also  points  to  a  common  origin  for 
them. 

Orion.  South  of  Taurus  is  the  constellation  Orion,  lying  across 
the  equator  between  the  fifth  and  sixth  hours  of  right  ascension. 
This  is  one  of  the  finest  regions  in  the  whole  heavens  for  a  study 
without  a  telescope.  In  the  winter  months,  in  the  early  evening,  it 
is  seen  in  the  southeastern  and  southern  sky.  In  the  northern  part 
of  it  is  the  ruddy  star  Betelgeuse,  and  about  20  degrees  southwest 
is  the  first-magnitude  star  Rigel.  About  midway  between  them  and 
almost  on  the  equator  is  a  row  of  second-magnitude  stars  running 
northwest  and  southeast  (in  Fig.  42  these  stars  are  a  little  above 
and  to  the  left  of  the  center),  which  constitutes  the  belt  of  Orion. 
From  the  southern  end  of  this  line  of  three  stars  are  three  fainter 
ones  going  off  toward  the  southwest.  These  constitute  the  sword  of 
Orion.  Careful  observation  shows  that  the  center  of  these  three  is  a 


98 


ASTRONOMY 


little  fuzzy.  It  is,  in  fact,  one  of  the  most  magnificent  spectacles  in 
the  whole  sky,  the  Orion  nebula.  Fig.  43  shows  this  splendid  object 
as  revealed  by  our  most  powerful  photographic  telescopes. 


Fig.  42.     The  Belt  and  Sword  of  Orion  and  the  Brilliant  Hi; •••! 

The  stars  in  this  part  of  the  sky  are  exceptionally  large  and 
remote  from  us.  The  star  Rigel,  shown  at  the  right  in  Fig.  42,  in 
light-giving  power  is  equal  to  10,000  such  suns  as  ours. 


100  ASTRONOMY 

Canis  Major.  Canis  Major  (the  Greater  Dog)  is  a  constellation 
southeast  of  Orion  and  contains  the  brightest  star  in  the  whole  sky, 
Sirius.  The  brightness  of  this  star  depends  to  a  considerable  extent 
upon  the  fact  that  it  is  relatively  near  to  us.  It  takes  the  light  from 
it  8.4  years  to  come  to  the  earth.  Expressed  otherwise  the  star  is 
47,000,000,000,000  miles  distant  from  us,  and  it  is  approaching  us  at 
the  rate  of  about  10  miles  per  second.  Sirius  is  really  overtaking  the 
sun,  for  the  solar  system  is  actually  moving  in  almost  exactly  the 
opposite  direction. 

It  was  found  in  1862  that  the  star  Sirius  had  a  very  faint  and 
distant  companion.  Observations  since  that  time  have  shown  that 
the  two  revolve  around  their  common  center  of  gravity  in  a  period 
of  about  50  years.  The  distance  of  the  two  components  from  each 
other  is  about  1,800,000,000  miles.  A  remarkable  fact  is  that  Sirius 
is  10,000  times  as  bright  as  its  companion,  while  its  mass  is  little 
more  than  twice  that  of  its  companion.  Their  combined  mass  is  a 
little  more  than  3.5  times  that  of  the  sun,  and  they  radiate  about  30 
times  as  much  light  as  the  sun. 

Gemini.  Gemini  (the  Twins)  is  the  fourth  zodiacal  constellation 
and  is  noteworthy  for  its  two  principal  stars,  Castor  and  Pollux. 
In  fact,  the  constellation  gets  its  name  from  these  two  objects  (twin 
stars),  which  are  of  nearly  the  same  size  and  about  4.5  degrees  apart. 
Castor  is  the  one  of  the  two  which  is  farther  north.  In  ancient 
times  Castor  seems  to  have  been  a  little  brighter  than  Pollux,  but 
now  the  condition  is  reversed.  This  may  be  due  to  the  fact  that 
Castor  is  receding  from  us  at  the  rate  of  4.5  miles  per  second,  while 
Pollux  is  approaching  at  the  rate  of  30  miles  per  second.  With  this 
large  relative  velocity  of  nearly  35  miles  per  second,  over  2,000  years 
have  been  required  for  any  conspicuous  change  in  their  relative 
brightness  to  take  place. 

TIME 

Definition  of  Equal  Intervals  of  Time.  It  is  very  difficult,  if 
not  impossible,  to  give  a  definition  of  time  itself.  So  far  as  we,  as 
thinking  beings,  are  concerned,  the  amount  of  time  which  passes 
depends  upon  our  intellectual  activity  in  the  interval.  As  an  illus- 
tration, it  may  be  mentioned  that  if  we  have  many  new  intellectual 
experiences,  as  for  example  when  we  travel,  the  time  seems  long; 


ASTRONOMY  101 

while  when  our  activities  are  in  their  customary  routine,  time  seems 
to  speed  rapidly.  The  same  thing  is  illustrated  by  the  well-known 
fact  that  a  year  seems  much  longer  to  a  young  person,  to  whom  the 
experiences  of  the  world  are  largely  new,  than  it  does  to  an  older 
person,  whose  habits  of  life  have  become  fixed  and  whose  new  experi- 
ences are  not  numerous.  Clearly,  however,  it  is  impossible  to  define 
the  length  of  time  by  means  of  the  varying  mental  activities  of  any 
individual  or  group  of  individuals. 

The  first  law  of  motion  previously  given  states  that  a  body 
subject  to  no  force  moves  with  uniform  speed  in  a  straight  line. 
Therefore,  by  definition,  it  follows  as  a  consequence  of  this  law,  or 
axiom,  that  two  intervals  of  time  are  equal  if  a  body,  subject  to  no 
force,  passes  over  equal  distances  in  them.  This  is  the  definition  of 
the  equality  of  two  intervals.  In  the  long  run  it  is  found  that  our 
mental  experiences  are  sensibly  in  harmony  with  it. 

The  difficulty  in  applying  the  definition  to  find  out  whether 
two  intervals  of  time  are  equal,  or  what  amounts  to  the  same  thing 
— the  relation  of  two  intervals — arises  from  the  fact  that  it  is  prac- 
tically impossible  to  find  a  moving  body  subject  to  no  force  and  to 
bring  it  under  observation.  Because  of  this  difficulty  an  indirect 
consequence  of  the  laws  of  motion  is  used.  It  follows  from  them, 
as  was  explained  above,  that  if  the  earth  is  subject  to  no  exterior 
forces  it  will  rotate  with  uniform  speed.  The  character  of  the  forces 
which  modify  its  rate  of  rotation  were  discussed  in  connection  with 
its  rotation.  It  was  seen  that  it  rotates  with  sensibly  uniform  speed, 
and  consequently  it  can  be  taken  as  the  actual  means  of  measuring 
intervals  of  time.  Using  the  rotation  of  the  earth  as  a  measure,  we 
agree  that  if  the  earth  turns  through  equal  angles  in  two  intervals  of 
time,  then  the  two  intervals  are  equal.  The  rotation  of  the  earth 
makes  the  sky  turn  apparently  from  west  to  east.  Consequently 
two  intervals  are  equal  if  the  sky,  in  its  apparent  motion,  turns 
through  equal  angles  in  them.  The  rotation  of  the  earth  is  the  actual, 
fundamental  means  of  measuring  time,  and  clpcks  are  regulated  by 
it.  The  observations  depend  upon  the  stars  and  for  this  reason  the 
discussion  of  this  topic  appropriately  is  taken  up  here  after  a  discus- 
sion of  the  rotation  of  the  earth  and  a  description  of  the  constellations. 

Sidereal  Time.  Sidereal  time  is  time  measured  by  the  rotation 
of  the  earth  with  respect  to  the  stars;  or,  by  the  apparent  motion 


102  ASTRONOMY 

of  the  stars  around  the  earth.  A  sidereal  day  is  the  time  it  takes 
a  meridian  of  the  earth  to  move  from  a  given  position  among  the 
fixed  stars  around  eastward  to  the  same  position  again;  or,  thinking 
of  the  stars  as  moving,  at  least  apparently,  it  is  the  interval  required 
for  the  fixed  stars  to  pass  from  the  meridian  around  the  earth  and 
back  to  it  again. 

The  sidereal  day  is  divided  into  24  sidereal  hours,  a  sidereal  hour 
into  60  sidereal  minutes,  and  a  sidereal  minute  into  60  sidereal  seconds. 

Solar  Time.  Our  activities  are  largely  regulated  by  the  day 
and  night.  Consequently,  time  for  practical  purposes  should  depend 
upon  the  apparent  motion  of  the  sun  around  the  earth  rather  than 
that  of  the  stars.  It  is  clear  that  since  the  sun  moves  eastward 
among  the  stars  about  one  degree  daily  in  its  apparent  annual  motion 
around  the  heavens,  the  diurnal  motions  of  the  stars  and  sun  are 
different.  Solar  time  is  time  measured  with  reference  to  the  sun. 
The  solarjiaj:  is  the  time  it  takes  the  meridian  to  pass  from  the  sun 
eastward  around  to  the  sun  again;  or,  the  time  it  takes  the  sun  to 
pass  from  the  meridian  apparently  around  westward  back  to  the 
meridian  again. 

Solar  day^.  and  sidereal  days  are  not  of  equal  length,  the  solar 
days  being  nearly  four  minutes  longer.  This  is  easily  understood 
from  the  fact  that  the  sun  moves  eastward  among  the  stars.  Sup- 
pose the  meridian  is  in  conjunction  with  the  sun  and  certain  stars, 
and  that  it  moves  eastward  and  around  to  the  same  stars  again. 
This  interval  constitutes  a  sidereal  day.  In  the  meantime,  how- 
ever, the  sun  will  have  moved  eastward  about  one  degree  and  the 
meridian  must  overtake  it  before  the  end  of  the  solar  day.  There- 
fore, the  solar  day  is  longer  than  the  sidereal  day,  and  the  difference 
is  the  time  it  takes  the  earth  to  rotate  about  one  degree.  The  earth 
rotates  360  degrees  in  24  hours,  or  15  degrees  in  one  hour.  There- 
fore, it  will  rotate  one  degree  in  one  fifteenth  of  an  hour,  or  in  four 
minutes.  That  is,  the  solar  day  is  about  four  minutes  longer  than 
the  sidereal  day. 

In  Fig.  44,  let  S  represent  the  sun  and  E^  the  position  of  the 
earth  at  one  time.  -Consider  the  meridian  m,  which  is  on  the  side 
toward  the  sun,  and  the  distant  star  s.  Suppose  that  in  one  sidereal 
day  the  earth  moves  forward  to  E2  (of  course,  the  distance  traveled 
is  greatly  exaggerated  in  the  figure).  This  means  that  the  meridian 


ASTRONOMY  103 

m  is  on  the  side  toward  the  star  again.  It  is  clear  from  the  figure 
that  the  earth  must  turn  through  the  angle  a  which  is  equal  to  the 
angle  which  it  has  moved  forward  in  its  orbit,  in  order  to  bring  m 
in  line  with  the  sun.  This  shows  why  the  solar  day  is  longer  than 
the  sidereal  day. 

Mean  Solar  Time.  It  has  been  stated  above  that  the  sidereal 
days  are  all  of  the  same  length  and  that  the  solar  days  are  longer 
than  the  sidereal  because  of  the  earth's  motion  forward  in  its  orbit. 
If  the  axis  of  the  earth  were  perpendicular  to  the  plane  of  its  orbit 
and  if  the  earth  moved  forward  in  its  orbit  at  a  uniform  speed,  the 
differences  between  the  sidereal  and  solar  days  would  all  be  the 
same.  That  is,  the  solar  days  would  also  all  be  of  the  same  length. 
But  the  earth's  orbit-is  an  ellipse  and  it  moves  in  such  away  that  the 
law  of  areas  is  fulfilled.  When  it  is  near  the  sun  it  moves  over  a 


Fig.  44.     The  Solar  Days  Are  about  4  Minutes  Longer  Than  the  Sidereal 
Days  Because  the  Earth  Revolves  around  the  Sun 

greater  angular  distance  in  a  given  time  than ^ when  it  is  far  from  it. 
It  follows  from  this  that  the  solar  days  are;  longest — at  least  so  far 
as  this  factor  affects  them — when  the  earth  Is  near  the  sun.  At  pre- 
sent the  earth  is  nearest  the  sun  in  our  winter  and  farthest  from  it  in 
our  summer.  Therefore,  the  solar  days  measured  from  noon  to  noon 
are  longer  in  the  winter  than  they  are  in  the  summer  of  the  northern 
hemisphere. 

There  is  another  reason  why  the  solar  days  vary  in  length. 
This  is  because  the  sun's  apparent  motion  eastward  in  the  sky  is 
not  along  the  equator  but  along  the  ecliptic.  The  difference  in  length 
between  the  sidereal  and  solar  days  depends  upon  the  distance  the 
sun  moves  eastward  along  the  equator.  Now,  let  us  suppose  for  the 
sake  of  simplicity  that  the  earth's  orbit  is  a  circle  and  that  the  earth 
moves  uniformly  along  its  circumference.  In  this  case  the  sun  will 


104 


ASTRONOMY 


seem  to  move  uniformly  along  the  ecliptic.  But  let  us  assume  that 
the  ecliptic  is  inclined  to  the  equator  by  23.5  degrees,  as  is  actually 
the  case.  In  Fig.  45,  the  straight  line  represents  the  equator  as  it 
would  be  obtained  by  spreading  the  celestial  sphere  out  on  a  plane. 
The  ecliptic  intersects  it  at  the  vernal  equinox,  V,  and  at  the  autumnal 
equinox,  A.  At  V  a  considerable  fraction  of  the  sun's  apparent 
motion  is  northward,  and  at  A  southward.  Consequently,  at  these 
points  its  motion  eastward  along  the  equator  is  less  than  the  average. 
But  when  the  sun  is  at  the  summer  solstice,  S,  and  at  the  winter 
solstice,  W,  its  motion  is  entirely  eastward  and  along  the  small 
circles,  viz,  along  those  declination  circles,  respectively,  23.5  degrees 
north  and  south  of  the  equator.  At  these  points  it  moves  eastward 
faster  than  the  average. 

Since  the  excess  in  length  of  the  solar  day  over  the  sidereal 
depends  upon  the  eastward  motion  of  the  sun,  it  follows  that  so  far 
as  the  causes  now  under  consideration  are  concerned  the  solar  days 


EQUATOR 


Fig.  45.     The  Sun  Moves  Eastward  Along  the  Ecliptic  Causing 
a  Variation  in  the  Lengths  of  the  Solar  Days 


are  shortest  when  the  sun  is  at  V  and  A,  and  longest  when  the  sun 
is  at  S  and  W.  The  sun  is  at  V  on  March  21,  at  A  on  September 
23,  at  S  on  June  22,  and  at  W  on  December  21.  So  far  as  this  cause 
is  concerned,  the  longest  days  are  in  the  summer  and  the  winter  and 
the  shortest  in  the  spring  and  autumn. 

The  actual  result  is  a  combination  of  these  two  factors  which 
influence  the  length  of  the  solar  day.  On  December  22  the  solar 
day  is  4  minutes  and  26.5  seconds  longer  than  the  sidereal  day  when 
expressed  in  sidereal  time.  The  solar  days  then  steadily  decrease 
until  March  26,  when  the-  solar  day  is  only  three  minutes  and  38 
seconds  longer  than  the  sidereal  day.  Then  they  increase  in  length 
until  June  20,  which  is  4  minutes  and  9.5  seconds  longer  than  the 
sidereal  day.  From  June  20  the  solar  days  again  decrease  in  length 
until  September  17,  which  is  the  shortest  day  of  the  whole  year, 
and  is  only  3  minutes  and  35.2  seconds  longer  than  the  sidereal 


ASTRONOMY  105 

day.  They  then  increase  until  December  22.  The  difference  in 
length  between  the  longest  and  shortest  day  in  the  year  is  therefore 
about  51.3  seconds  of  sidereal  time. 

The  differences  in  the  lengths  of  the  solar  days  are  not  very 
great  and  it  might  be  supposed  that  they  could  be  neglected.  But 
nowadays  the  best  clocks  are  made  to  run  so  accurately  that  they 
much  more  than  reveal  this  difference,  and  besides  the  difference 
accumulates.  Consequently,  it  is  not  practicable-  to  use  the  solar 
day.  This  leads  to  a  definition  of  what  is  called  mean  solar  time. 
The  mean  solar  day  is  the  average  of  all  the  true  solar  days  in  the  year. 
In  sidereal  time  its  length  is  24  hours,  3  minutes  and  56.556 
seconds  It  is  divided  into  24  mean  solar  hours,  an  hour  into  60 
mean  solar  minutes,  and  a  minute  into  60  mean  solar  seconds.  This 
is  the  actual  day  in  ordinary  use. 

Standard  Time.  Each  meridian  on  the  earth  has  its  own  time 
because  the  sun  crosses  each  meridian  at  a  separate  time.  Therefore, 
if  we  were  to  use  mean  solar  time  only  those  places  which  are  on  the 
same  meridian  would  have  the  same  time.  It  is  clear  that  very  great 
confusion  would  result  from  this.  It  was  stated  above  that  a  degree 
of  longitude  at  latitude  40°  is  about  53  miles.  That  is,  at  our  latitude 
there  is  a  difference  of  four  minutes  in  mean  solar  time  for  every  53 
miles,  or  one  minute  for  every  13  miles.  While  for  many  purposes  so 
slight  a  variation  as  this  would  not  be  important,  yet  in  the  running 
of  trains  and  boats  it  would  be  of  the  highest  importance.  This  is 
especially  true  in  a  country  where  most  of  the  great  trunk  lines  of 
railways  run  in  an  easterly  and  westerly  direction. 

In  order  to  avoid  the  confusion  resulting  from  each  meridian 
having  its  own  time  the  railways,  in  1885,  by  common  agreement, 
adopted  the  same  time  for  a  strip  of  country  between  meridians 
about  15  degrees  apart.  The  hour  adopted  was  the  correct  mean 
solar  time  for  the  meridian  approximately  through  the  center  of  the 
strip.  Therefore,  the  error  on  each  side  increases  to  about  one-half 
an  hour  at  the  extremity  of  the  strip.  Since  one  degree  is  about 
53  miles  in  our  latitude,  the  width  of  these  strips  averages  about 
800  miles.  For  convenience  the  strips  are  not  of  uniform  width  and 
do  not  strictly  follow  the  meridians.  It  is  clear  that  it  would  be  incon- 
venient for  a  railway  system  to  change  time  except  at  one  of  the 
divisions  of  the  road.  Therefore,  the  place  of  the  change  of  time  is 


106 


ASTRONOMY 


made  to  agree  with  the  ends  of  divisions  on  the  railway.  The  accom- 
panying map,  Fig.  46,  shows  the  time  zones  in  the  United  States. 
The  easternmost  division  is  called  eastern  time,  and  has  the 
time  of  the  meridian  which  is  75  degrees  west  of  the  Greenwich 
Observatory.  This  meridian  runs  through  Philadelphia.  Next  comes 
central  time,  the  mean  solar  time  of  the  90th  meridian  west  of  Green- 
wich, which  runs  through  St.  Louis.  Then  follows  mountain  time, 
the  time  of  the  105th  meridian,  which  passes  near  Denver;  and  on 
the  Pacific  Coast  they  use  the  mean  solar  time  of  the  120th  meridian, 
called  Pacific  time.  This  meridian  passes  about  100  miles  east  of 
San  Francisco. 


Fig.  46.     The  Standard  Time  Divisions  in  the  United  States 

The  difference  between  standard  time  and  mean  solar  time  can 
be  calculated  when  one  knows  his  distance  from  the  fundamental 
time  meridian  of  his  zone,  because  13  miles  corresponds  to  a  difference 
of  about  one  minute. 

If  one  is  east  of  the  fundamental  meridian  the  sun  crosses  his 
meridian  before  it  does  that  of  the  fundamental  meridian.  Con- 
sequently, by  the  sun  the  time  is  later  than  it  is  by  standard  time. 
That  is,  he  would  say  that  standard  time  is  slow.  For  example, 
Chicago  is  about  100  miles  east  of  the  meridian  through  St.  Louis, 


ASTRONOMY  107 

and  therefore  standard  time  at  Chicago  is  about  eight  minutes  slow. 
West  of  the  meridian  standard  time  is  fast. 

Civil  and  Astronomical  Days.  The  civil  day  begins  at  midnight 
and  ends  at  midnight  mean  solar  time.  It  is  clear  that  it  is  most 
convenient  to  have  the  date  change  when  there  are  the  least  activities, 
especially  in  the  business  world,  and  the  midnight  change  satisfies 
these  conditions  with  sufficient  accuracy. 

The  astronomical  day,  on  the  other  hand,  begins  at  noon  and 
ends  at  noon,  mean  solar  time.  The  reason  for  this  is  that  it  is  most 
convenient  to  have  the  astronomical  day  change  when  fewest  astro- 
nomical observations  are  made.  About  the  only  ones  that  can  be 
made  at  noon  are  those  of  the  sun. 

Place  of  Change  of  Date.  Suppose  one  should  start  at  any 
place  and  go  around  the  earth  in  a  westward  direction.  On  each 
day  of  his  travel  the  sun  would  cross  his  meridian  later  than  if  he 
had  stayed  at  home.  In  making  the  full  circuit  he  would  lose  in  this 
fashion  exactly  one  day.  But  if  he  should  go  around  the  earth  in 
the  other  direction  the  sun  would  cross  his  meridian  earlier  each 
day  than  if  he  had  stayed  at  home,  and  the  number  of  days  meas- 
ured by  the  number  of  times  the  sun  crossed  his  meridian  would  be 
one  greater  than  if  he  had  not  made  the  journey.  It  is  clear  from 
this  that  if  one  goes  around  the  earth  in  the  westward  direction  he 
must  drop  one  day  from  his  reckoning  in  order  to  be  in  harmony 
with  those  who  have  not  made  the  journey,  and  if  he  goes  eastward 
he  must  add  one  day  to  preserve  harmony.  It  is  convenient  to  have 
the  place  of  the  change  of  day  a  fixed  one  which  is  well  agreed  upon. 
It  is  also  obvious  that  it  is  convenient  to  have  this  where  there 
are  few  inhabitants,  for  one  can  see  the  confusion  which  would  arise 
if  on  one  side  of  the  line  through  a  populous  district,  as  for  example 
a  large  city,  people  had  one  day  and  date  and  on  the  other  side  a 
day  and  date  differing  by  one  day. 

The  place  where  the  date  is  changed  is  about  180  degrees  from 
the  meridian  of  Greenwich.  This  passes  through  the  Pacific  Ocean 
and  near  very  few  land  areas.  There  is  no  meridian  in  the  whole 
earth  that  would  cause  less  confusion.  However,  the  change  is  not 
made  precisely  at  the  180th  meridian  throughout  its  length.  People 
who  settled  certain  islands  along  this  meridian  going  eastward  from 
Europe  naturally  took  their  day  and  date  with  them,  while  those 


108 


ASTRONOMY 


going  in  the  other  direction  also  took  their  day  and  date.  These 
disagreed  by  one  day  when  they  met  in  the  Pacific  Ocean.  On  this 
account  there  are  certain  irregularities  which  are  exhibited  in  Fig.  47. 
The  Sidereal  Year.  Just  as  there  are  different  kinds  of  days 
depending  upon  whether  we  consider  the  rotation  of  the  earth  with 
respect  to  the  stars  or  sun,  so  there  are  different  kinds  of  years.  The 
period  of  revolution  of  the  earth  with  respect  to  the  stars  is  called 
the  sidereal  year.  It  is  the  time  required  for  the  sun  to  pass  appar- 
ently from  any  position  among  the  stars  back  to  the  same  position 


IflO      165     150     135     120     105     90       75 


105°    120°    135°    150°    165°    150°    165°     160°    135°    120"    105°    90*     78 


Fig.  47.     The  Line  at  Which  Travelers  Change  Their  Day  and 

Date,  Dropping  a  Day  If  Going  Westward  and  Adding 

a  Day  If  Going  Eastward 

again.  In  mean  solar  time  the  length  of  the  sidereal  year  is  365  days, 
6  hours,  9  minutes,  and  8.97  seconds,  or  just  a  little  more  than 
365.25  days. 

The  Tropical  Year.  The  tropical  year  is  the  time  it  takes  the 
earth  to  move  from  the  vernal  equinox  around  to  the  vernal  equinox 
again.  Since  the  equinoxes  have  a  precession,  this  year  is  a  little 
shorter  than  the  sidereal  year.  In  mean  solar  time  its  actual  length 
is  365  days,  5  hours,  45  minutes,  and  45.51  seconds.  Thus  it  is 
seen  to  be  about  20  minutes  shorter  than  the  sidereal  year.  In  order 


ASTRONOMY  109 

to  keep  the  calendar  fixed  with  respect  to  the  seasons  it  is  necessary 
to  use  the  tropical  year.  As  a  matter  of  fact,  this  is  the  year  in  ordi- 
nary use  rather  than  the  sidereal  year. 

The  Calendar.  In  very  ancient  times  the  calendar  was  largely 
based  on  the  motions  of  the  moon,  which  determined  the  times  of 
religious  ceremonies.  The  sun  has  the  same  appearance  from  day 
to  day  and  probably  was  regarded  as  somewhat  commonplace.  The 
moon  goes  through  an  interesting  and  striking  change  of  phases, 
which  recur  frequently  enough  so  that  they  are  easily  remembered, 
and  the  fact  that  they  systematically  repeat  was  easily  discovered. 
It  was  natural  to  define  time  by  the  phases  of  the  moon,  which  con- 
tinually vary  but  constantly  recur. 

When,  however,  records  were  kept  over  longer  intervals  of  time 
it  was  found  that  the  method  was  not  a  very  convenient  one.  In 
the  first  place  there  is  not  an  integral  number  of  months  in  the  year, 
the  number  being  between  twelve  and  thirteen.  Therefore,  a  cal- 
endar based  on  the  months  has  the  seasons  continually  shifting  with 
respect  to  it.  The  calendar  of  the  ancient  Egyptians  was  of  this 
character.  As  the  science  of  astronomy  was  developed  they  grad- 
ually turned  to  a  calendar  based  on  the  year  as  a  fundamental  unit, 
and  left  the  month  largely  out  of  consideration.  In  the  year  46  B.  c. 
the  Roman  calendar  was  reformed  by  Julius  Caesar  with  the  assist- 
ance of  the  Alexandrian  astronomer  Sosigenes.  This  calendar  which 
is  known  as  the  Julian  calendar,  was  entirely  independent  of  the 
moon,  and  the  year  consisted  of  365  days,  with  a  leap  year  every 
fourth  year  of  366  days.  The  extra  day  was  added  at  the  end  of 
February.  This  mode  of  reckoning  makes  the  average  year  exactly 
365.25  days.  It  is  seen  from  the  result  given  above  that  the  length 
of  the  tropical  year  is  about  eleven  minutes  shorter  than  this.  It 
follows  from  this  that  the  Julian  calendar  falls  one  day  behind  in  the 
course  of  128  years.  By  1582  the  calendar  was  in  error  more  than 
12  days  and  the  matter  was  getting  serious.  In  that  year  Pope 
Gregory  XIII  introduced  a  slight  change.  Twelve  days  were  omitted 
from  that  year  and  it  was  agreed  that  thereafter  three  leap  years 
out  of  every  four  centuries  should  henceforth  be  omitted.  This  rule 
again  is  not  quite  exact,  for  the  Julian  calendar  falls  behind  three 
days  in  3  X  128  =  384  years  instead  of  400  years.  Yet  the  error  does 
not  amount  to  a  day  until  after  more  than  3,000  years  have  elapsed. 


110  ASTRONOMY 

Although  the  Gregorian  calendar  is  sufficiently  accurate  for  3,000 
years,  it  will  some  time  have  to  be  still  further  corrected. 

The  rule  for  the  leap  year  is  very  simple.  All  years  whose 
date  numbers  are  not  divisible  by  4  are  years  of  365  days.  Those 
years  whose  date  numbers  are  divisible  by  4  are  leap  years  unless 
they  are  also  exactly  divisible  by  100.  Those  years  whose  date 
numbers  are  divisible  by  100  are  not  leap  years  unless  they  are 
exactly  divisible  by  400,  then  they  are  leap  years.  This  is  as  far 
as  the  rule  has  been  extended  up  to  the  present  time. 

While  the  Gregorian  calendar,  or  at  least  a  slight  modification 
of  it,  keeps  the  seasons  fixed  with  respect  to  the  year,  yet  it  is  in 
many  ways  imperfect.  It  is  certainly  inconvenient  to  have  months 
of  different  lengths,  to  have  the  months  in  different  years  begin  on 
different  days  of  the  week,  and  to  have  our  numerous  holidays  and 
festival  days,  for  this  reason,  continually  shifting  through  the  week. 
There  are  exceptions,  of  course,  in  those  which  are  fixed  on  certain 
days  irrespective  of  the  date,  as  for  example  Easter  and  Thanks- 
giving. Recently  suggestions  have  been  made  for  the  improve- 
ment of  the  calendar. 

THE  MOON 

The  Moon's  Apparent  Motion  among  the  Stars.  The  stand- 
ard method  of  determining  the  real  motions  of  a  heavenly  body 
is  first  to  get  its  apparent  motions  from  the  actual  observations ;  and 
second,  to  get  indirectly  its  real  motions.  The  moon  apparently 
moves  eastward  among  the  stars,  completing  a  circuit  of  the  sky  in 
a  little  less  than  a  month.  Its  apparent  orbit  is  a  great  circle  on  the 
celestial  sphere,  though  it  does  not  coincide  with  the  equator.  It 
is  near  the  ecliptic,  deviating  from  it  by  only  five  degrees,  nine  min- 
utes. When  the  moon  is  in  that  part  of  its  orbit  where  the  ecliptic 
is  north  of  the  equator  it  crosses  the  meridian  in  its  diurnal  motion 
high  in  the  sky,  and  when  it  is  at  that  part  of  its  orbit  where  the 
ecliptic  is  south  of  the  equator  it  crosses  the  meridian  in  its  diurnal 
motion  low  in  the  sky.  Since  it  makes  the  complete  circuit  of  its 
orbit  in  a  month,  there  are  times  each  month  when  it  crosses  the 
meridian  high  and  others  when  it  crosses  it  low.  When  it  crosses 
the  meridian  high  it  rises  in  the  northeast  and  sets  in  the  northwest, 
just  as  the  sun  rises  in  the  northeast  in  the  summer  time  and  sets 


ASTRONOMY  111 

in  the  northwest.  When  it  crosses  the  meridian  at  a  low  altitude 
it  rises  in  the  southeast  and  sets  in  the  southwest,  as  the  sun  does 
in  the  winter  time. 

The  period  of  revolution  of  the  moon  around  the  earth  can  be 
determined  by  its  motion  with  respect  to  the  stars  or  its  motion 
with  respect  to  the  sun.  The  time  it  takes  the  moon  to  go  from  a 
certain  place  among  the  stars  around  the  sky  back  to  the  same  place 
again  is  called  the  sidereal  month.  It  is  found  from  the  observations 
that  its  length  is  27  days,  7  hours,  43  minutes,  and  11.55  seconds. 
The  time  it  takes  it  to  go  around  the  sky  with  respect  to  the  sun  is 
called  the  synodic  month.  This  is  clearly  longer  than  the  sidereal 
month,  for  if  the  moon  were  at  one  time  in  conjunction  with  the  sun 
and  certain  stars  and  then  moved  eastward  around  the  sky  back  to 
the  same  stars  again,  the  sun  in  the  meantime  (27.3  days)  would 
have  moved  eastward  about  27  degrees.  The  synodic  month  then 
is  longer  than  the  sidereal  by  the  time  it  takes  the  moon  to  move 
over  this  distance  eastward  and  to  overtake  the  sun.  Since  the 
moon  makes  a  circuit  of  the  heavens  in  27  days,  it  follows  that  its 
eastward  motion  is  on  the  average  about  13  degrees  a  day.  Conse- 
quently it  will  take  it  a  little  more  than  two  days  to  overtake  the 
sun  after  it  has  arrived  back  at  the  same  stars  again.  That  is,  the 
synodic  month  is  a  little  more  than  two  days  longer  than  the  sidereal 
month.  It  is  found  from  the  observations  that  the  length  of  the 
sidereal  month  is  29  days,  12  hours,  44  minutes,  and  2.86  seconds. 

The  Moon's  Phases.  The  moon  shines  only  by  reflected  light 
and  its  phases  as  seen  from  the  earth  depend  upon  its  position  rela- 
tive to  the  earth  and  sun.  Where  the  sun's  rays  do  not  illuminate 
it,  it  is  dark  the  same  as  the  earth  is  on  its  night  side.  Fig.  48  shows 
the  reason  of  the  phases.  In  this  figure  the  sun's  rays  come  in  from 
the  right  toward  the  left  in  sensibly  parallel  lines.  The  right  side 
of  the  earth  is  the  day  side,  and  similarly  the  right  side  of  the  moon 
is  the  day  side  of  the  moon.  When  the  moon  is  at  M 1  the  side 
toward  the  earth  is  the  dark  side  and  the  phase  is  called  the  new 
moon.  The  appearance  of  it  is  indicated  in  Nt.  In  about  a  week 
the  moon  passes  forward  in  its  orbit  in  the  direction  indicated  by  the 
arrow  to  the  point  M 2.  At  this  time  half  of  the  illuminated  portion 
is  visible  to  the  earth  and  its  appearance  is  indicated  in  Nz.  This  is 
at  the  first  quarter  and  the  moon  is  at  the  half-moon  phase.  In 


112  ASTRONOMY 

another  week  it  moves  forward  to  M3,  when  the  illuminated  side  is 
toward  the  earth  and  it  appears  as  N3.  At  the  third  quarter  the 
moon  is  at  M t,  and  has  the  appearance  of  JV4. 

Let  us  consider  the  matter  a  little  more  carefully.  Suppose  the 
earth  rotates  in  the  direction  indicated  by  the  arrow.  Then  as  the 
observer  passes  from  the  day  side  of  the  earth  to  the  night  side  he  is 
at  0  at  sunset.  If  he  observes  the  new  moon  at  sunset  it  will  be  in 
the  same  direction  as  the  sun,  or  in  the  western  sky.  At  the  time  of 
half-moon  at  the  first  quarter  when  the  sun  is  in  the  western  sky, 
it  is  seen  from  the  diagram  that  the  moon  is  on  the  observer's  merid- 
ian and  the  light  side  of  it  is  toward  the  west.  When  the  moon  is 
full  the  observer  sees  the  sun  setting  in  the  west  and  the  full  moon 


Q      $ 

Fig.  48.     The  Reason  for  the  Moon's  Phases 

rising  in  the  east.     Everyone  knows  that  these  results  are  in  perfect 
harmony  with  the  facts  of  observation. 

When  the  moon  is  nearly  new,  that  is,  when  it  is  between  MI 
and  M2,  it  presents  a  thin  crescent,  convex  toward  the  western  sky. 
At  this  time,  however,  the  rest  of  it  can  be  dimly  seen.  It  is  clear 
from  a  study  of  the  diagram  that  the  earth  has  phases  as  seen  from 
the  moon  similar  to  those  of  the  moon  as  seen  from  the  earth,  the 
only  difference  being  that  they  are  opposite.  That  is,  when  the 
moon  is  new,  as  seen  from  the  earth,  the  earth  is  full  as  seen  from 
the  moon.  When  the  moon  is  in  the  position  under  consideration 
and  nearly  new  the  earth  as  seen  from  it  is  nearly  full.  Conse- 
quently, the  moon  is  to  some  extent  illuminated  by  the  light  that 
goes  to  it  from  the  earth.  The  darker  part  of  the  moen  that  we 


ASTRONOMY  113 

see  faintly  when  it  is  at  this  phase,  is  illuminated  to  a  slight  extent 
by  the  earth-shine.  This  earth-shine  is  about  20  times  full  moon- 
light. 

Distribution  of  Sunlight  and  Moonlight.  The  amount  of  light 
received  from  the  moon  by  the  earth  is  of  little  importance  except 
at  the  time  of  full  moon.  It  follows  from  the  preceding  section  that 
the  full  moon  is  exactly  opposite  the  sun  in  the  sky.  Consequently, 
when  the  moon  is  nearly  full  it  is  above  the  horizon  at  night  while 
the  sun  is  below  it,  and  is  below  the  horizon  while  the  sun  is  above. 
Because  of  this  fact  the  light  is  more  equally  distributed  throughout 
the  24  hours  than  it  would  be  if  they  were  both  on  the  same  side  of 
the  earth  at  this  phase.  This  is  not  only  true,  but,  since  the  full 
moon  is  opposite  the  sun  in  the  sky,  when  the  sun  is  at  the  part  of 
the  ecliptic  south  of  the  equator,  the  full  moon  is  at  the  part  of  the 
ecliptic  north  of  the  equator.  This  means  that  at  that  time  of  the 
year,  viz,  the  winter,  when  we  receive  the  least  sunlight,  we  receive 
the  most  moonlight,  and  in  the  summer  when  we  receive  the  most 
sunlight,  we  receive  the  least  moonlight.  Everyone  has  the  dim 
impression  that  the  moon  shines  more  brightly  in  the  winter  than  in 
the  summer,  and  such  is  a  fact,  as  this  discussion  shows.  Also,  in 
the  winter  the  full  moon  rises  far  in  the  northeast  and  in  the  summer 
in  the  southeast.  Year  after  year  it  is  almost  exactly  the  same  and 
no  changes  in  the  weather  conditions  can  be  ascribed  to  the  chang- 
ing relations  of  the  moon  relatively  to  the  sun  and  earth. 

The  polar  regions  of  the  earth  are  conceived  of  as  being  places 
of  perpetual  darkness  and  desolation  for  six  months  each  year. 
This  conception  is  slightly  in  error,  because  after  the  sun  has  actually 
set  there  is  a  considerable  interval  in  which  the  twilight  is  strong 
enough  to  enable  men  to  carry  on  all  ordinary  pursuits.  Also,  since 
when  the  sun  is  below  the  horizon  it  is  far  south,  the  full  moon  is  corre- 
spondingly north  of  the  equator  and  is  above  the  horizon.  There- 
fore, for  half  of  the  dark  period  the  moon  between  the  first  and  third 
quarters  circulates  in  the  sky  and  lights  up  the  surface  of  the  earth. 
It  follows  from  this  that  the  long  night  in  the  polar  regions  is  not 
quite  so  gloomy  as  it  is  often  pictured. 

Distance  of  the  Moon.  In  order  to  determine  the  size  "and 
character  of  the  moon,  and  also  the  character  of  its  orbit,  it  is  neces- 
sary to  know  its  distance.  The  method  of  finding  the  distance  of 


114  ASTRONOMY 

the  moon  is  similar  to  that  used  by  surveyors  in  finding  the  distance 
across  an  impassable  gulf  or  chasm.  Suppose  the  wavy  lines  in  Fig. 
49  represent  the  banks  of  an  impassable  chasm,  and  that  a  surveyor 
wishes  to  know  accurately  the  distance  from  B  to  M.  He  takes  a 
point  A  on  the  bank  of  the  chasm  which  is  visible  from  both  B  and 
M,  and  then  to  the  left  on  the  bank  lays  down  the  lines  DA  and  CB 
in  such  a  way  that  DC  shall  be  parallel  to  AB.  He  then  draws  a 
line  from  A  to  E  parallel  to  BC.  He  measures  the  distances  AB, 
DE,  and  EA.  Since  by  construction  the  triangle  AMB  is  similar 
to  DAE,  he  has  the  proportion  BM  :  BA  =  EA  :  ED,  which  solved 
gives  BM=(BAxEA)  + ED.  It  is  clear  from  this  that  the  dis- 
tance across  the  impassable  chasm  can  be  measured  as  accurately 

as  the  distances  BA,  EA,  and 
ED  are  measured  on  the  level 
land. 

As  a  matter  of  fact  the  meas- 
urement can  be  made  a  little  more 
simply  than  has  been  described. 
The  method  is  to  set  up  at  B  a 
surveyor's  instrument,  which  con- 
rig.    49.      Measurement    of    the    Distance        d<;t<5    nf    fl    tplp«r>nr»P    that    nan    KP 
across  an  Impassable  Chasm 

turned    horizontally  and    which 

has  degrees  marked  off  indicating  the  direction  at  which  it  is 
pointed.  After  the  telescope  is  accurately  adjusted  it  is  pointed  at 
M  and  then  turned  and  pointed  at  A.  The  readings  of  the  circle  at 
the  two  different  times  give  the  angle  MBA.  Then  the  instrument 
is  set  up  at  A  and  pointed  at  M  and  then  at  B.  The  readings  in 
this  case  give  the  angle  MAB.  Now  the  distance  AB  is  measured. 
Then,  in  the  triangle  MBA,  the  angles  A  and  B  and  the  included 
side  are  known.  It  follows  from  plane  geometry  that  the  triangb 
is  determined  by  these  three  parts.  Trigonometry  enables  one  to 
compute  the  remaining  sides  when  these  three  are  given.  There- 
fore, by  trigonometry,  which  is  based  on  such  considerations  funda- 
mentally as  the  measurements  of  DEA  described  above,  the  dis- 
tance BM  can  be  computed. 

In  Fig.  50,  let  the  circle  E  represent  the  earth  and  suppose  A 
is  the  position  of  an  observer  in  the  northern  hemisphere.  The  line 
AZ  points  to  his  zenith.  Suppose  the  moon  is  on  his  meridian; 


ASTRONOMY  115 

therefore,  it  will  be  to  the  south.  He  has  a  telescope  set  up  at  A 
fixed  so  that  it  can  move  in  the  plane  of  the  meridian.  It  is  pointed 
up  at  Z  and  then  turned  over  until  it  points  to  the  moon  M.  The 
readings  of  a  circle  similar  to  that  on  the  surveyor's  instrument 
give  the  angle  ZAM.  By  subtraction  the  interior  angle  M  A  B  can  be 
found.  Suppose  there  is  another  observer  on  the  same  meridian  in 
the  southern  hemisphere  at  B.  His  zenith  is  in  the  direction  BZf. 
He  sets  up  a  telescope  and  measures  the  corresponding  angle.  Now 
consider  the  triangle  MAB.  The  angle  at  A  and  the  angle  at  B 
are  known  by  the  measurements,  and  since  the  observer  at  A  knows 
how  far  he  is  north  of  the  equator  and  the  one  at  B  how  far  he  is 


I 


Fig.  50.     Measurement  of  the  Distance  to  the  Moon  by  Observations  from 
Two  Points  on  the  Earth's  Surface 

south  of  the  equator,  and  since  the  size  of  the  earth  is  known,  the 
straight  line  AB  is  also  known.  Consequently,  in  the  triangle  we 
have  given  two  angles  and  the  included  side,  and  the  triangle  can 
be  solved  precisely  as  in  the  case  of  the  surveyor  finding  the  distance 
across  the  chasm.  This,  fundamentally,  is  the  way  the  distance  from 
the  earth  to  the  moon  is  found.  It  must  be  understood  that  in 
carrying  out  the  measurements  many  artifices  are  used  to  secure 
results  of  the  highest  order  of  accuracy.  The  point  insisted  on  here 
is  that  the  result  is  in  no  sense  whatever  guess-work,  but  that  it  is 
based  upon  careful  measurements,  and  is  in  reality  a  measurement 
as  much  as  is  the  measurement  of  any  distance  on  the  surface  of  the 
earth.  The  percentage  of  error  in  our  knowledge  of  the  distance  of 
the  moon  from  the  earth  is  actually  much  less  than  the  percentage 
of  error  of  any  of  the  ordinary  distances  we  know  on  the  earth.  For 
example,  it  is  rarely  that  the  officials  of  a  railway  know  the  length  of 
its  track  between  two  cities  with  the  same  relative  degree  of  accuracy 
that  astronomers  know  the  distance  from  the  earth  to  the  moon. 


116  ASTRONOMY 

It  is  observed  that  the  measurement  of  the  distance  from  the 
earth  to  the  moon  depends  upon  the  measurements  of  two  angles 
and  the  line  joining  two  places,  A  and  B.  Our  knowledge  of  the 
length  of  this  line  depends  upon  knowing  the  size  of  the  earth.  If 
there  are  any  errors  in  our  knowledge  of  the  earth's  dimensions  they 
introduce  corresponding  errors  in  our  knowledge  of  the  distance 
from  the  earth  to  the  moon.  If,  for  some  reason,  we  have  obtained 
too  large  a  diameter  for  the  earth  then  the  distance  to  the  moon 
will  be  too  large  by  the  same  factor.  At  the  present  time  so  many 
measurements  of  arcs  on  the  earth  have  been  made  that  we  know 
its  size  with  a  very  high  degree  of  precision. 

From  the  methods  just  explained  it  has  been  found  that  the 
mean  distance  from  the  earth  to  the  moon  is  238,840  miles.  This 
distance  is  about  ten  times  as  far  as  around  the  earth.  One  who  has 
traveled  over  any  considerable  portion  of  the  earth's  surface  knows 
how  great  it  is.  We  can  get  a  mental  picture  of  it  by  calculating 
how  long  it  would  take  objects  traveling  with  known  speed  to  go 

©— : '- , . Z 

Fig.  51.     The  Earth  and  Moon  and  Their  Distance  Apart  on  the  Same  Scale 

over  so  great  a  distance.  It  is  known  that  sound  travels  with  a  high 
velocity.  The  puff  of  smoke  from  a  gun  is  seen  and  almost  imme- 
diately the  report  is  heard.  Or,  perhaps  better,  a  flash  of  lightning 
is  seen  in  the  sky  and  in  only  a  few  seconds  the  report  of  the  thunder 
is  heard.  It  is  found  from  observations  and  experiments  that  sound 
travels  a  mile  in  about  five  seconds,  or  at  the  rate  of  720  miles  an 
hour.  It  follows  from  this  and  the  distance  to  the  moon  that,  if  there 
were  an  explosion  on  the  moon  and  the  sound  of  it  could  come  to  us, 
it  would  require  14  of  our  days  and  nights  to  reach  us.  Of  course, 
sound  can  not  come  from  the  moon  to  the  earth  because  the  atmos- 
phere does  not  extend  over  that  distance.  In  Fig.  51  the  earth  and 
distance  to  the  moon  are  shown  to  a  relative  scale  and  on  this  figure 
the  depth  of  the  atmosphere,  supposing  it  to  be  100  miles,  would  be 
only  y$T  of  an  inch. 

If  a  train  could  come  from  the  moon  to  the  earth  running  at  the 
rate  of  a  mile  a  minute,  night  and  day,  without  any  stops  whatever,  it 
would  require  166  days  for  it  to  come  to  us.  These  calculations  give  a 
better  conception  than  mere  figures  of  the  great  distance  to  the  moon. 


ASTRONOMY  117 

The  Moon's  Actual  Motion.  It  follows  from  the  moon's  apparent 
motions  and  its  distance  that  it  moves  around  the  earth  in  an  orbit 
whose  circumference  is  about  1,500,680  miles.  Dividing  this  by  the 
sidereal  period,  it  is  found  that  the  moon's  orbital  velocity  averages 
about  2,290  miles  per  hour,  or  3,357  feet  per  second.  It  is  found 
from  the  observations  of  the  apparent  diameter  of  the  moon  that 
its  distance  from  the  earth  varies  somewhat.  Plotting  its  orbit  by 
the  method  used  in  determining  the  shape  of  the  earth's  orbit  around 
the  sun,  it  is  found  that  the  moon's  path  is  also  elliptical  and  that 
the  earth  is  at  one  of  its  foci.  It  does  not  move  uniformly  in  its 
orbit,  but  moves  in  such  a  way  that  the  radius  from  the  center  of 
the  earth  to  it  sweeps  over  areas  which  are  proportional  to  the  time. 

The  moon  is  carried  forward  with  the  earth  in  its  motion  around 
the  sun.  The  motion  of  the  earth  is  about  50  times  as  fast  as  that  of 


Fig.  52.     The  Motion  of  the  Moon  Relative  to  the  Sun 

the  moon  in  its  orbit.  Consequently,  when  the  moon  is  between  the 
earth  and  sun,  as  at  M  in  Fig.  52,  and  its  motion  is  backward  with 
respect  to  the  earth,  it  is  actually  moving  forward  very  fast  with 
respect  to  the  sun.  The  distance  from  the  earth  to  the  moon  is  about 
TOU  of  the  distance  from  the  earth  to  the  sun.  It  follows  from  this 
that  the  motion  of  the  moon  toward  the  sun  and  away  from  it,  as  it 
crosses  the  earth's  orbit,  is  relatively  insignificant  compared  to  its 
motion  forward  as  it  is  taken  with  the  earth  around  the  sun.  The 
consequence  of  this  is  that  the  moon's  orbit  is  concave  toward  the 
sun  at  every  point  and  sensibly  like  that  of  the  earth. 

Up  to  this  point  we  have  spoken  as  though  the  earth  moved 
around  the  sun  in  an  elliptical  orbit.  As  a  matter  of  fact,  it  is  the 
center  of  gravity  of  the  earth  and  moon  which  describes  this  curve, 
these  two  bodies  revolving  around  their  center  of  gravity  in  a  month. 
This  point  is  only  3,000  miles  from  the  center  of  the  earth,  and  is 
therefore  in  round  numbers  1,000  miles  below  its  surface. 


118 


ASTRONOMY 


The  moon  always  keeps  the  same  face  toward  the  earth.  Con- 
sequently it  rotates  on  its  axis  once  while  it  passes  around  the  earth; 
that  is,  its  period  of  rotation  is  the  same  as  that  of  its  revolution. 
In  Fig.  48  the  side  of  the  moon  which  is  toward  the  left  when  the 
moon  is  at  If !  has  turned  around  so  that  it  is  toward  the  right  when 
the  moon  is  at  Ms. 

Size  of  the  Moon.  The  mean  apparent  diameter  of  the  moon 
is  31  minutes  8  seconds,  the  apparent  diameter  varying  by  a  little 
more  than  two  minutes  because  of  the  eccentricity  of  the  moon's 
orbit.  When  the  apparent  size  of  an  object  is  known  and  its  distance 
from  the  observer  is  known,  it  is  a  simple  matter  by  trigonometry  to 
compute  its  actual  size.  It  turns  out  that  the  actual  diameter  of 
the  moon  is  2,163  miles.  This  result  is  known  with  the  same  degree 
of  certainty  as  the  distance  to  the  moon.  The  diameter  of  the  moon 

is  about  27  per  cent  of  that 
of  the  earth,  and  their  rela- 
tive dimensions  are  shown  to 
the  same  scale  in  Fig.  53. 

Since  the  surfaces  of  sim- 
ilar bodies  are  as  the  squares 
of  their  dimensions  the  sur- 
face of  the  moon  is  about 
-&  that  of  the  earth;  and 
since  their  volumes  are  as 

the  cubes  of  their  dimensions  the  volume  of  the  moon  is  about  A 
that  of  the  earth. 

When  the  moon  is  on  the  observer's  meridian  it  is  nearer  the 
observer  than  when  it  is  on  his  horizon  by  about  4,000  miles.  Thus, 
in  Fig.  54,  0  is  about  4,000  miles  nearer  M  than  P  is.  Therefore,  the 
moon  ought  to  look  larger  when  it  is  near  the  meridian  than  when  it 
is  at  the  horizon.  As  a  matter  of  actual  fact  it  is  found  by  measure- 
ment with  a  telescope  that  the  moon  is  apparently  larger  near  the 
meridian  than  when  it  is  on  the  horizon  and  the  difference  is  in  har- 
mony with  these  figures.  But  without  an  instrument  the  moon 
certainly  appears  larger  at  the  horizon.  The  explanation  of  this 
peculiar  appearance,  which  is  directly  opposed  to  the  actual  facts, 
is  that  when  the  moon  is  high  in  the  sky  there  is  nothing  with  which 
to  compare  its  distance,  and  the  observer  underestimates  greatly 


Fig.  53.     The  Earth  and  Moon  Shown  on  the 
Small  Scale 


ASTRONOMY  119 

its  distance  from  us.  Our  judgment  of  the  size  of  an  object  depends 
upon  two  things,  its  apparent  diameter  and  our  knowledge  of  its 
distance  from  us.  •  K  we  think  it  is  very  close  we  unconsciously  esti- 


Fig.  54.     Diagram  Illustrating  Change  of  Size  of  Moon 

mate  it  as  being  of  small  size,  while  if  we  think  of  it  as  being  very 
far  away  we  judge  that  it  is  large.  It  is  not  difficult  to  bring  a  spider 
web  near  the  eye  and  to  force  into  the  consciousness  a  belief,  first, 
that  it  is  something  very  near  when  it  appears  very  small,  as  it  actually 
is;  and  second,  that  it  is  something  very  far  away  when  it  has  the 
appearance  of. a  large  cable,  instead  of  a  very  minute  thread.  Now 
our  estimate  of  the  real  size  of  the  moon,  or  any  other  celestial 
object,  depends  in  a  similar  way  upon  our  unconscious  estimate  of 
its  distance.  As  has  been  said,  for  some  reason  when  the  moon  is 
high  in  the  sky  we  judge  that  it  is  near  to  us,  and  consequently  it 
appears  small.  When  it  is  near  the  horizon  it  is  easy  to  see  that  it 
is  beyond  the  buildings  and  trees  which  are  visible  in  its  direction, 
and  that  forces  into  our  consciousness  the  knowledge  that  it  is  far 
away.  Then  unconsciously  we  picture  it  as  large.  The  actual 
measurements  with  instruments  prove  that  the  estimate  that  the 
moon  is  larger  when  near  the  horizon  than  when  high  in  the  sky,  is 
purely  subjective,  and  the  explanation  for  this  has  just  been  given. 
Mass  of  the  Moon.  The  mass  of  the  moon  relatively  to  that 
of  the  earth  is  determined  by  the  distance  of  the  earth  from  the 
center  of  gravity  of  the  earth  and 

.  •  W '_.£.  ^ / & 

moon.     1  he  principle  is  the  same         A 

as  that  of  balancing  weights  on  Fig  55    Weighing  the  Moon 

the  arms  of  a  lever.     In  Fig.  55 

let  W  and  w  represent  two  weights  at  distances  L  and  I  from  the 

fulcrum  F.     Then  by  the  principle  of  the  lever  W  X  L  =  w  X  L 

And  so  in  the  case  of  the  earth  and  moon,  the  mass  of  the  earth  times 


120  ASTRONOMY 

the  distance  from  its  center  to  the  center  of  gravity  of  the  earth  and 
the  moon  equals  the  mass  of  the  moon  times  its  distance  from  the 
center  of  gravity  of  the  earth  and  moon.  The  center  of  gravity  of 
the  earth  and  moon  being  determined  from  the  observations  of  the 
motion  of  the  earth  around  the  sun,  which  determine  the  point 
describing  the  elliptical  orbit,  it  is  possible  to  find  the  mass  of  the 
moon  in  terms  of  the  mass  of  the  earth.  It  turns  out  that  the  mass 
of  the  earth  is  81.7  times  that  of  the  moon.  It  follows  from  the 
volume  of  the  moon  given  above,  and  the  density  of  the  earth  given 
in  the  description  of  the  earth,  that  the  density  of  the  moon  is  3.4 
times  that  of  water. 

The  weight  of  a  body  on  the  surface  of  the  earth  depends  upon 
the  mass  of  the  earth  and  the  distance  of  the  surface  of  the  earth 
from  its  center.  In  particular,  the  weight  of  a  body  is  directly  pro- 
portional to  the  mass  of  the  earth,  and  inversely  proportional  to  the 
square  of  its  distance  from  the  center  of  the  earth.  The  correspond- 
ing thing  is  true  on  the  moon.  Using  the  mass  of  the  moon  and  the 
size  of  it  given  above,  it  is  found  that  an  object  on  the  surface  of 
the  moon  weighs  only  one-sixth  as  much  as  the  same  object  would 
on  the  surface  of  the  earth.  This  refers  to  weighing  on  a  spring  bal- 
ance. If  the  object  were  weighed  with  an  ordinary  balance  scale, 
where  a  small  weight  is  used  to  balance  the  body  weighed  it  would, 
of  course,  wreigh  the  same  as  on  the  earth,  because  the  change  in 
pull  on  the  body  weighed  and  the  balancing  weight  would  be  in  the 
same  ratio.  It  follows  from  the  fact  that  a  body  weighs  only  one- 
sixth  as  much  on  the  moon  as  it  would  upon  the  earth,  that  the  same 
force  there  would  throw  it  six  times  as  high.  If  a  man  can  jump 
five  feet  high  upon  the  earth,  the  same  man  on  the  moon,  if  he  could 
live  there  and  exert  the  same  energy,  could  jump  30  feet  high.  Vol- 
canic activity  on  the  moon  would  throw  matter  six  times  as  high  as 
the  same  activity  on  the  earth.  Since  matter  weighs  less  on  the 
moon,  mountains  could  be  piled  six  times  as  high  before  the  rock 
would  crush  and  break  out  at  their  bottoms.  Perhaps  this  partly 
explains  why  mountains  are  so  very  high  and  rugged  on  the  moon, 
as  we  shall  presently  see. 

Atmosphere  of  the  Moon.  The  moon  has  little  or  no  atmosphere. 
This  is  proved  by  the  fact  that  its  surface  always  stands  out  with 
remarkable  distinctness,  there  never  being  the  slightest  evidence  of 


ASTRONOMY  121 

clouds  or  obscuring  vapor.  It  is  also  shown  by  the  fact  that  when 
the  moon  passes  between  us  and  the  sun  there  is  no  luminous  ring 
around  it  as  there  would  be  if  it  had  an  atmosphere.  The  differ- 
ence is  conspicuous  when  the  planet  Venus  passes  between  us  and 
the  sun.  This  planet  has  an  atmosphere  and  the  illuminated  ring 
of  its  gaseous  envelope  is  visible  when  it  is  in  a  line  with  the  sun. 

One  might  well  ask  why  the  moon  has  no  atmosphere.  The 
theory  has  been  suggested  that  it  has  been  gradually  absorbed  by 
the  rocks  of  the  surface.  This  is  not  very  probable  because  while 
the  rocks  may  absorb  some  atmosphere,  on  the  other  hand,  they 
also  give  it  forth.  As  they  disintegrate  they  liberate  as  a  rule  large 
quantities  of  gas.  Also  there  are  irregularities  on  the  surface  of  the 
moon  which,  if  interpreted  as  indicating  volcanic  activity  in  past 
times,  means  that  large  volumes  of  gases  have  been  given  forth  from 
its  interior. 

A  better  explanation,  and  one  which  is  almost  certainly  correct, 
is  that  the  moon  has  not  sufficient  gravitative  power  to  hold  an 
atmosphere.  As  was  explained  above  in  connection  with  the  atmos- 
phere of  the  earth  and  the  kinetic  theory  of  gases,  there  is  a  tendency 
of  the  molecules  of  an  atmosphere  to  escape  from  the  bodies  which 
they  surround  by  darting  off  into  space.  The  gravitative  power  of 
the  moon  is  so  slight  that  the  opportunities  for  escape  are  much 
greater  than  in  the  case  of  the  earth.  Consequently,  it  is  not 
unreasonable  to  suppose  that  the  atmosphere  of  the  moon,  if  it  ever 
had  one,  has  been  lost  into  space,  molecule  by  molecule.  Of  course, 
there  is  no  guarantee  that  at  any  time  in  its  history  it  ever  had  an 
atmosphere  comparable  to  that  of  the  earth.  But  in  view  of  the 
activities  that  its  surface  shows  were  once  taking  place  there,  it 
seems  probable  that  it  would  now  have  a  greater  atmosphere  than 
.observation  shows  exists,  if  it  had  not  been  lost  in  this  manner. 

Light  and  Heat  Received  by  the  Earth  from  the  Moon.  Direct 
observations  of  the  amount  of  light  and  heat  received  from  the 
moon  show  that  at  full  moon  we  get  about  -gnrlinnr  as  much  light 
and  heat  from  the  moon  as  from  the  sun.  The  average  amount  of 
light  and  heat  received  from  the  moon  compared  to  that  received 
from  the  sun  is  very  much  less  than  this,  probably  not  more  than 
one-fourth  as  great.  Therefore,  it  follows  that  we  receive  more  light 
and  heat  from  the  sun  in  15  seconds  than  we  do  from  the  moon  in 


122  ASTRONOMY 

a  whole  year.  The  passing  of  a  cloud  between  the  earth's  surface 
and  the  sun  for  a  few  minutes  reduces  the  amount  of  light  and  heat 
received  more  than  it  would  be  reduced  if  the  moon  were  taken 
from  our  sky  for  a  year. 

It  follows  from  these  figures  that  the  moon  does  not  have  a 
sensible  effect  in  raising  the  temperature  of  the  earth.  It  is  seen 
from  this  how  absurd  it  is  to  suppose  that  hot  spells  or  cold  spells 
depend  in  any  way  upon  the  moon.  As  a  matter  of  fact,  the  discus- 
sion of  observations  covering  a  very  long  time  do  not  show  any 
certain  relation  of  any  kind  between  the  state  of  the  weather  and  the 
phases  of  the  moon.  So  far  as  can  be  determined  from  observations 
extending  over  a  century  there  is  no  more  likelihood  of  its  freezing 
or  raining  or  being  hot  at  one  phase  of  the  moon  than  at  another. 

Temperature  of  the  Moon.  The  average  distance  of  the  moon 
from  the  sun  is  about  as  great  as  that  of  the  earth,  and  consequently 
if  its  atmosphere  were  the  same  and  its  rotation  were  the  same  its 
climate  would  be  similar  to  that  of  the  earth.  The  most  important 
difference  in  this  connection  between  the  earth  and  moon  is  that  the 
moon  has  no  atmosphere.  Therefore,  the  day  side  of  the  moon  is 
subject  to  the  intense  rays  of  the  sun  with  no  protection  of  clouds 
or  atmosphere,  and  the  night  side  loses  its  heat  rapidly  and  the 
temperature  falls  very  low. 

It  was  explained  above  that  the  moon  keeps  the  same  face 
toward  the  earth  all  the  time,  and  consequently  that  it  turns  on  its 
axis  once  in  a  month.  Its  day  is,  therefore,  a  synodic  month  of  28.5 
of  our  days.  This  long  period  of  rotation  adds  to  the  extremes  of 
temperature  which  the  moon  already  is  shown  to  have  because  of 
the  absence  of  an  atmosphere  surrounding  it.  For  more  than  14 
of  our  days  its  surface  is  subject  to  the  burning  rays  of  the  sun, 
and  then  for  more  than  14  of  our  days  it  is  in  darkness.  During  the 
long  period  it  receives  light  and  heat  from  the  sun  its  temperature 
rises  very  high,  probably  reaching  the  boiling  point. ,  During  the  long 
night  its  temperature  falls  very  low,  perhaps  200°  or  250°  below  zero. 
The  lowest  natural  temperature  ever  known  upon  the  earth,  even  in 
arctic  regions,  is  about  90  degrees  below  zero. 

The  temperature  of  the  moon  can  not  be  found  without  some 
difficulty.  We  have  instruments  which  can  measure  as  small  amounts 
of  heat  as  the  moon  sends  to  us  but  the  difficulty  arises  in  this  case 


ASTRONOMY  123 

from  the  fact  that  the  heat  we  receive  from  the  moon  is  partly 
radiated  heat  and  more  largely  reflected  sunlight  and  heat.  It  is 
not  possible  to  fully  separate  the  two.  If  it  were,  and  we  had  the 
amount  of  heat  the  moon  radiates  to  us,  we  should  be  able  to  obtain 
its  temperature  with  a  considerable  degree  of  accuracy.  The  best 
time  for  doing  it  and  the  one  in  which  the  reflected  light  and  heat 
do  not  seriously  bother  is  when  the  moon  passes  into  the  earth's 
shadow.  Just  before  it  enters  the  shadow  it  has  been  subject  to  the 
rays  of  the  sun  falling  .almost  perpendicularly  upon  it.  It  enters 
the  shadow  and  the  sun's  light  and  heat  are  cut  off.  (See  Fig.  56.) 
The  only  heat  which  the  observer  at  0  receives  from  the  moon  at 
this  time  is  that  which  the  moon  radiates  because  its  temperature 
has  been  raised  before  it  entered  the  shadow  of  the  earth.  This  heat 
has  been  measured  and  from  it  we  have  arrived  at  our  ideas  concerning 


Fig.  56.     The  Earth's  Shadow  and  Eclipse  of  the  Moon 

the  temperature  of  the  moon.  It  is*  an  interesting  and  significant 
fact  that,  during  the  two  hours  required  for  the  moon  to  pass  through 
the  earth's  shadow,  its  temperature  falls  so  low  that  at  the  end  of 
the  eclipse  we  do  not  receive  sensible  quantities  of  heat  from  it. 

The  moon  is,  therefore,  to  be  thought  of  as  a  body  whose  surface 
is  subject  to  alternating  periods  of  burning  and  freezing  temperatures. 
Clearly,  it  is  impossible  for  life  such  as  we  have  upon  the  earth  to 
exist  on  such  a  body.  There  is  every  reason  to  believe  that  it  is  a 
dead  world  and  probably  that  it  has  always  been  without  life  of 
any  form. 

Surface  Conditions  on  the  Moon.  The  moon  appears  to  be  an 
object  of  light  and  dark  areas  as  viewed  without  a  telescope.  Through 
a  telescope  the  same  regions  are  still  apparent,  but  it  is  found  that 
those  which  are  light  are  extremely  rough  while  those  which  are  dark 
are  relatively  smooth.  Fig.  57  shows  a  photograph  of  the  full  moon 
in  which  to  some  extent  the  light  areas  and  the  dark  areas  can  be  made 
out,  and  can  be  seen  to  be,  respectively,  rough  and  smooth. 


124  ASTRONOMY 

The  most  striking  feature  on  the  moon  is  a  great  number  of 
circular  pits  varying  in  diameter  from  a  few  thousand  feet  up  to 
more  than  100  miles.  These  depressions  are  called  craters.  It  must 
not  be  inferred,  however,  from  the  name  that  they  are  necessarily 
similar,  either  in  their  general  features  or  in  their  origin,  to  the 


Fig.  57.     The  Full  Moon  Photographed  at  the  Yerkes  Observatory 

volcanic  craters  we  have  upon  the  earth.  They  are  usually  deep 
depressions  in  the  surface  of  the  moon  with  no  evidence  of  lava  flows 
around  them,  and  often,  if  not  generally,  with  high  mountains  in 
their  interiors.  In  many  cases  if  their  rims  were  piled  into  the 
depressions  they  would  not  be  filled. 

The  question  of  the  origin  of  the  lunar  craters  is  not  easy  to 
answer  with  any  degree  of  certainty.  Arguing  from  analogy  with 
the  earth  one  might  suppose  they  are  of  volcanic  origin.  However, 


ASTRONOMY  125 

the  peculiarities  noted  above  are  against  this  theory.  It  seems  less 
improbable  to  suppose  that  they  have  been  formed  by  explosions  of 
vast  accumulations  of  gas  in  the  interior  of  the  moon.  If  we  suppose 
its  temperature  was  high  near  the  surface,  and  that  in  contracting 
large  quantities  of  gas  gathered  here  and  there  at  shallow  depths,  it 
is  not  altogether  unreasonable  to  suppose  that  because  of  the  high 
temperature  the  gas  would  occasionally  tear  its  way  out  through  the 
surface  with  explosive  violence.  In  such  an  explosion  matter  would 
be  thrown  far  and  wide,  depending  upon  its  violence,  and  much  of 
it  would  fall  back  into  the  cavity  from  which  the  gas  escaped.  It 
is  not  entirely  unreasonable  to  suppose  the  craters  may  have  origi- 
nated somewhat  in  this  fashion.  If  they  have,  the  violence  of  the 
explosion  is  attested  by  the  long  cracks  in  the  rocks  radiating  from 
the  biggest  craters  and  in  some  cases  reaching  to  a  distance  of  more 
than  a  thousand  miles.  They  are  conspicuously  shown  around  several 
craters  in  Fig.  57. 

Another  hypothesis  as  to  the  origin  of  craters,  which  has  perhaps 
some  merit,  is  that  they  were  formed  by  the  impact  of  huge  meteorites 
striking  on  the  moon  from  without.  In  order  to  form  in  this  manner 
those  large  craters  which  are  approximately  100  miles  in  diameter, 
it  would  be  necessary  that  meteorites  very  many  miles  in  diameter 
should  strike  the  moon.  According  to  this  theory  the  craters  should 
be  depressions,  as  they  are  seen  to  be,  and  there  is  no  reason  why  the 
matter  which  constitutes  their  rims  should  fill  them  if  it  were  put 
on  the  inside.  One  serious  objection  to  this  hypothesis  is  that  the 
craters  are  all  very  nearly  circular.  If  they  were  formed  by  the  impacts 
of  meteorites  it  would  be  expected  that  some  of  them  would  strike 
the  moon  glancing  blows  and  make  long  streaks  instead  of  circular 
pits.  If  the  impact  theory  is  the  true  explanation  of  the  origin  of  the 
lunar  craters,  the  heat  generated  by  the  impact  of  the  meteorites  is 
not  a  negligible  quantity  in  accounting  for  their  peculiarities.  A 
meteorite  striking  the  surface  of  the  moon  with  the  velocity  at  which 
meteors  enter  the  earth's  atmosphere,  would  generate  enough  heat  to 
liquefy  and  volatilize  a  considerable  fraction  of  the  matter  in  the 
neighborhood  of  the  point  where  it  struck.  This  sudden  heating  of 
the  matter  in  the  interior  of  the  crater  pits  would  cause  secondary 
explosions  and  might  perhaps  elevate  the  mountains  which  are  found 
in  them. 


Fig.  58.     The  Crater  Theophilus  64  Miles  Across  and  18,000  Feet  Deep 


Fig.  59.     The  Great  Crater  Clavius  and  Surrounding  Region 


128  ASTRONOMY 

If  the  craters  of  the  moon  had  their  origin  in  the  impacts  of  the 
meteorites  from  the  outside  the  question  arises  why  the  earth  has 
not  been  subject  to  a  similar  bombardment.  These  two  bodies  have 
been  associated  throughout  their  evolution  as  distinct  bodies  and 
there  is  no  reason  assignable  why  the  moon  should  have  been  more 
subject  to  the  impact  of  meteorites  than  the  earth.  The  reason 


Fig.  60.     The  Lunar  Apennines,  Named  by  Galileo  Who  First  Saw  Them 

for  the  absence  of  such  evidence  on  the  earth  is  that  the  earth 
has  an  atmosphere  surrounding  it  and  is  nearly  covered  with 
water.  These  elements  disintegrate  the  rocks,  and  in  the  course  of 
the  millions  of  years  which  have  elapsed  since  such  a  bombardment 
has  taken  place,  if  indeed  it  ever  did  take  place,  the  evidences  of 
these  impacts  have  been  totally  destroyed.  On  the  other  hand,  on 


ASTRONOMY  129 

the  moon  there  is  no  atmosphere  and  no  water  and  the  rocks  would 
be  preserved  as  they  were  originally  formed.  The  chief  disintegrating 
effects  are  the  extremes  of  temperature  which  have  been  described 
above. 

One  of  the  most  interesting  craters  is  Theophilus,  a  photograph 
of  which  is  shown  in  Fig.  58.  This  crater  is  64  miles  across.  Its 
depth  is  from  16,000  to  19,000  feet.  This  result  is  obtained  by  meas- 
urements of  the  length  of  the  shadows  in  its  interior,  knowing  the 
altitude  of  the  sun  as  seen  from  the  moon  when  the  photograph  was 
taken.  It  is  simply  the  problem  of  determining  the  height  of  a  building 
from  the  length  of  its  shadow  when  the  altitude  of  the  sun  is  known. 
In  the  interior  of  Theophilus  there  are  mountains  which  are  about 
16,000  feet  high.  In  the  photograph  their  shadows  can  be  seen 
stretching  off  to  the  left,  long,  sharp,  and  spire-like.  They  show  the 
rugged  character  of  these  mountains.  They  stand  up  from  the  floor 
of  the  crater  higher  than  any  mountains  on  the  earth  reach  above  the 
plateaus  on  which  they  rest. 

There  are  many  places  on  the  moon  where  a  number  of  genera- 
tions of  craters  can  be  seen.  In  Fig.  59  it  is  possible  to  see  large  old 
craters  and  new  ones  formed  on  their  remains  and  in  their  interiors. 

The  moon  has  a  number  of  mountain  ranges  and  very  many 
isolated  peaks.  One  of  the  most  remarkable  ranges  is  the  Apennines, 
Fig.  60,  named  by  Galileo  after  the  Apennines  of  Italy.  These 
mountains  are  extremely  rugged  and  very  high,  many  of  their  peaks 
towering  more  than  20,000  feet  above  the  plateaus  on  which  they  stand. 

Fig.  61  shows  a  photograph  of  one  of  the  dark,  relatively  smooth 
places  called  by  Galileo  M are  Serenitatis,  or  the  Serene  Sea.  With  his 
little  telescope  he  was  not  able  to  discern  the  craters  which  we  see 
in  it  and  the  ranges  of  hills  which  are  running  across  it.  Since  we 
have  mountains  on  the  earth  and  also  on  the  moon,  he  came  to  the 
conclusion  that  these  two  objects  were  very  similar.  Therefore, 
it  was  natural  for  him  to  suppose  that  there  were  seas  on  the  moon 
as  well  as  on  the  earth,  and  these  smooth  places  were  the  only  things 
which  could  be  interpreted  as  being  vast  bodies  of  water.  It  is  now 
clear  that  there  is  no  water  there  whatever,  and  there  is  no  evidence 
that  there  ever  has  been  any.  In  all  probability  the  side  of  the  moon 
which  we  never  see  is  in  all  essential  respects  similar  to  that  which 
is  toward  the  earth. 


ASTRONOMY  131 

Besides  the  craters,  the  mountains,  and  the  plains  of  the  moon, 
there  are  a  number  of  remarkable  long,  narrow,  and  deep  cracks  in 
its  surface  called  rills.  In  some  respects  they  resemble  the  Grand 
Canon  of  the  Colorado  more  than  anything  else  on  the  earth.  But 
the  Grand  Canon  of  the  Colorado  was  made  by  the  river  cutting 
its  way  through  the  rock;  while  the  rills  on  the  moon  have  certainly 
had  a  different  origin.  They  may  be  simply  cracks  in  the  rock  of 
the  shrinking  mass.  If  the  cracks  were  made  on  the  moon  by  the 
breaking  rocks  it  was  certainly  shaken  by  severe  earthquakes,  for 
it  is  well  known  that  earthquakes  here  on  the  earth  are  usually,  if 
not  always,  produced  by  the  breaking  of  the  rocks  of  the  earth's 
crust  and  their  slipping  on  each  other.  For  example,  the  destruc- 
tive earthquake  in  San  Francisco  in  1906  was  due  to  a  crack  nearly 
parallel  to  the  coast  several  hundred  miles  in  length,  and  the  slip- 
ping of  the  rock  on  one  side  of  the  crack  past  that  on  the  other  side. 

Eclipses  of  the  Moon.  When  the  moon  passes  into  the  earth's 
shadow  it  is  eclipsed.  It  might  be  imagined  from  Fig.  48  that  the 


Fig.  62.     The  Moon  Is  Not  Eclipsed  Every  Month  Because  Its  Orbit 
Is  Inclined  to  the  Ecliptij 

moon  would  be  eclipsed  every  time  it  is  full.  The  reason  it  is  not 
is  because  the  plane  of  its  orbit  is  inclined  to  the  ecliptic  about  five 
degrees.  Since  the  sun  apparently  travels  on  the  ecliptic  the  shadow 
of  the  earth  travels  along  the  ecliptic.  In  Fig.  62  let  the  straight 
line  represent  the  ecliptic  and  the  curve  the  moon's  orbit.  Let  the 
circle  S  represent  the  cross  section  of  the  shadow  of  the  earth  at  the 
distance  of  the  moon.  Let  M  represent  the  moon.  The  point  A 
is  the  place  where  the  moon's  orbit  crosses  the  ecliptic  from  south 
to  north,  and  is  called  the  ascending  node,  while  D,  the  other  p!ace 
where  the  moon's  orbit  crosses  the  ecliptic,  is  called  the  descending 
node.  If  the  moon  passes  the  earth's  shadow  when  it  is  near  A  and 
D,  clearly  it  will  pass  through  the  shadow  and  be  eclipsed.  If  it 
passes  the  shadow  when  it  is  between  A  and  D  and  not  when  near 
one  of  these  points,  it  will  miss  the  earth's  shadow  and  will  not  be 
eclipsed. 


132  ASTRONOMY 

The  moon  travels  around  the  earth  about  13  times  in  a  year 
and  consequently  passes  the  earth's  shadow  about  13  times  in  a 
year.  At  two  of  these  times  it  passes  the  shadow  near  the  points 
A  and  Z),  and  at  these  times  the  moon  is  eclipsed.  The  other  eleven 
times  the  shadow  of  the  earth  is  so  far  from  A  and  D  that  the  moon 
does  not  pass  through  it.  It  is  easy  to  see,  therefore,  why  the  moon 
is  not  eclipsed  every  month,  and  why  it  is  eclipsed  twice  a  year  on 
dates  which  are  six  months  apart. 

The  points  A  and  D  are  not  fixed  on  the  ecliptic.  The  attrac- 
tion of  the  sun  for  the  moon  disturbs  its  orbit  and  causes  the  points 
A  and  D  to  move  backward  along  the  ecliptic.  For  this  reason  the 
eclipse  at  A  occurs  earlier  each  succeeding  year;  and  similarly  at 
D.  The  points  A  and  D  make  a  revolution  in  about  19  years. 
Consequently,  the  time  of  eclipses  shifts  throughout  the  whole  y< 
in  a  period  of  19  years. 

The  chief  scientific  uses  of  an  eclipse  of  the  moon  are  to  deter- 
mine its  temperature,  as  described  above,  and  to  search  for  its  possi- 
ble satellites.  When  the  moon  is  new  it  is  in  the  direction  of  the  sun 
and  faint  objects  can  not  be  seen  in  its  vicinity.  When  it  is  full  it 
gives  so  much  light  that  faint  objects  can  not  be  seen  near  it.  But 
when  it  is  eclipsed  its  light  is  diminished  to  such  an  extent  that  if 
there  were  any  small  satellites  revolving  about  it  we  should  have  a 
good  chance  of  photographing  them.  Up  to  the  present  time  no 
satellites  of  the  moon  have  been  discovered  and  there  is  no  particular 
reason  for  believing  they  exist. 

Eclipses  of  the  Sun.  If  the  orbit  of  the  moon  were  exactly  in 
the  plane  of  the  ecliptic,  the  sun  would  be  eclipsed  at  every 
moon.  But  the  inclination  of  the  moon's  orbit  causes  this  phenom- 
enon to  be  relatively  rare.  In  Fig.  62  we  may  think  of  S  as  repre- 
senting the  sun  itself  instead  of  the  earth's  shadow.  The  moon 
passes  the  sun  13  times  a  year,  but  passes  between  the  earth  and  the 
sun  only  when  the  passage  is  made  near  A  or  D.  Therefore,  the 
eclipses  of  the  sun  occur  only  twice  in  the  year,  six  months  apart. 
This  statement  requires  a  slight  correction  because,  if  the  sun  is 
eclipsed  when  it  is  to  the  left  of  A,  it  is  possible  under  certain  circum- 
stances for  the  moon  to  make  a  revolution  of  the  sky  and  partially 
to  eclipse  it  again  when  it  is  to  the  right  of  A  and  still  near  to  it. 
The  circumstances  are  similar  relative  to  the  point  D.  It  is  possible, 


ASTRONOMY  133 

therefore,  to  have  four  eclipses  of  the  sun  in  a  year.  Hence,  taking 
the  lunar  and  solar  eclipses  together  it  is  possible  to  have  six  in  a 
year,  two  of  the  moon  and  four  of  the  sun. 

Relative  Number  of  Eclipses  of  Sun  and  Moon  as  Observed 
from  Any  One  Place.  In  Fig.  63,  suppose  S  represents  the  sun,  E 
the  earth,  and  M±  the  moon  at  the  time  it  is  eclipsed.  This  eclipse 
can  be  seen  from  the  half  of  the  earth  on  the  side  toward  it.  Since 
it  takes  the  moon  about  two  hours  to  pass  through  the  earth's  shadow, 
the  eclipse  is  visible  not  only  to  half  the  earth,  but  also  to  the  part 
which  is  rotated  into  view  of  it  during  the  two  hours.  Since  there 
are  two  eclipses  of  the  moon  a  year  and  each  one  is  visible  to  at  least 
half  the  earth,  it  follows  that  on  the  average  at  every  place  on  the 
earth  one  eclipse  of  the  moon  per  year  is  visible. 

Let  M2  represent  the  position  of  the  noon  when  the  sun  is 
eclipsed.  The  sun  will  be  eclipsed  only  within  the  part  of  the  shadow 


Fig.  63.     Diagram  for  Explaining  the  Reason  of  Eclipses  of  the  Moon  and  Sun 

cone  from  the  moon  which  strikes  the  earth,  i.  e.,  at  the  region  P. 
The  moon,  passing  around  the  earth,  causes  this  shadow  to  strike 
across  the  earth  in  a  path  whose  width  is  generally  less  than  100 
miles,  and  whose  length  is  a  few  thousand  miles. 

Fig.  64  shows  the  path  of  a  total  eclipse  of  the  sun  as  given  in 
the  nautical  almanac.  It  is  seen  from  this  how  small  a  portion  of 
the  surface  of  the  earth  is  totally  shadowed  during  an  eclipse.  It 
follows  that  in  spite  of  the  fact  that  there  are  more  eclipses  of  the 
sun  than  of  the  moon,  the  number  observed  at  any  one  place  is  very 
much  less.  Everyone  who  has  paid  any  attention  to  celestial  phe- 
nomena has  seen  an  eclipse  of  the  moon,  but  comparatively  few 
people  have  seen  a  total  eclipse  of  the  sun.  While  the  path  of  totality 
is  very  narrow,  there  is  a  large  region  from  which  the  sun  is  seen  as 
partially  eclipsed.  A  partial  eclipse  is  relatively  of  small  interest 
as  compared  with  a  total  eclipse. 


134 


ASTRONOMY 


Fig.  65  shows  the  paths  of  total  eclipses  of  the  sun  from  1894 
to  1973.  It  is  seen  from  this  map  that  there  are  large  regions  of 
the  earth  from  which  a  total  eclipse  is  not  visible,  and  in  fact  that 
only  a  small  part  of  the  whole  earth  is  eclipsed  at  all,  during  the  80 
years  which  it  covers.  The  fact  that  total  eclipses  of  the  sun  are 
startling  and  not  very  frequent  led  the  ancients  carefully  to  record 
them.  Their  records  have  thus  been  of  assistance  to  historians 
in  some  cases  in  fixing  the  dates  in  ancient  chronology.  If  an 


LOrtG/TUDC      WEST 


GREEMWICH  LOMC/rUDE  FAST  <y" GttErtW/CH 

^       »^       "Q        '^.        „  o^         °^          °Q  °Q 

5_     ^ s       ^        ^        «\i         ^ > 


Fig.  64.     Path  of  a  Total  Eclipse  of  the  Sun 

ancient  chronicler  described  an  eclipse  at  a  certain  place  and  stated 
the  date  of  it  in  his  system  of  counting  time,  it  is  possible  to  locate 
that  date  in  our  system  of  counting  time,  because  the  astronomers 
computing  back  across  the  centuries  can  tell  the  historians  at  what 
time  an  eclipse  in  that  part  of  the  world  could  have  occurred. 

One  of  the  uses  of  the  eclipses  of  the  sun  is  the  determination 
of  the  period  of  the  moon  around  the  earth.  It  is  clear  that  at  the 
time  of  an  eclipse  the  moon  is  exactly  between  the  earth  and  the  sun. 
At  some  later  time  it  is  again  between  the  earth  and  the  sun  and 
there  is  another  eclipse.  If  the  whole  interval  and  the  number  of 
revolutions  the  moon  has  made  in  the  meantime  are  known,  it  is 


ASTRONOMY 


135 


possible  to  find  the  period  of  one  revolution  by  dividing  the  nvholtf 
time  by  the  number  of  revolutions.  The  advantage  in  this  method 
lies  in  the  fact  that  eclipses  have  been  observed  for  a  very  long  time 
and  the  errors  of  observations  are  divided  up  because  of  the  very 
many  revolutions  the  moon  has  made  in  the  meantime. 

A  second  use  of  eclipses  of  the  sun  is  the  study  of  the  atmosphere 
and  corona  of  the  sun.  The  corona  is  visible  only  at  the  time  of 
total  eclipses  and  is  therefore  subject  to  study  only  during  the  few 
minutes  of  eclipses  which  occur  at  rare  intervals. 

A  third  use  of  solar  eclipses  is  that  during  the  periods  of  totality 


TRACKS  OF 

TOTAL  ECLIPSES 

OF  THE 

SUN  1894-1973. 


Fig.  65.     Paths  of  Total  Eclipses  of  the  Sun 

a  search  can  be  made  for  possible  planets  revolving  so  close  to  the 
sun  that  they  are  not  visible  unless  its  bright  rays  are  screened  off. 
A  screen  in  the  atmosphere  covering  it  is  of  no  use,  for  the  illuminated 
atmosphere  around  is  brighter  than  such  objects  would  be.  But  the 
distant  moon  is  beyond  our  atmosphere  and  when  it  eclipses  the  sun 
it  makes  the  sky  dark,  allowing  the  region  near  the  sun  to  be 
searched,  particularly  by  photography,  for  undiscovered  planets. 
So  far  none  have  been  discovered,  and  now  so  many  photographs 
have  been  secured  during  eclipses  that  it  is  improbable  that  any  with 
a  diameter  exceeding  100  miles  exists  in  close  vicinity  of  the  sun. 


THE    MOON'S    DISK 
The  view  shows  the  disk  at  9J  days,  photographed  with  40-inch  refractor 


ASTRONOMY 

PART  III 


THE  SOLAR  SYSTEM 

Members  of  the  Solar  System.  The  members  of  the  solar 
system  are  the  sun,  the  planets,  and  their  satellites,  the  planetoids, 
the  comets,  and  the  meteors,  though  it  may  be  that  many  of  the 
comets  and  meteors  are  only  temporary  members  of  the  solar  family. 
The  sun  is  in  all  respects  the  most  important  body  in  the  system. 
Its  gravitative  power  holds  the  planets  in  their  orbits,  and  its  light 
and  heat  illuminate  and  warm  them.  It  is  impossible  to  consider 
the  planets  and  comets  without  considering  their  relations  to  the 
sun,  but  it  is  quite  possible  to  discuss  the  sun  without  particular 
reference  to  the  planets.  For  the  present  we  shall  be  interested  in  all 
those  members  of  the  system  except  the  sun. 

There  are  eight  planets  in  the  solar  system,  which  in  the  order 
of  their  distances  from  the  sun  are  Mercury,  Venus,  Earth,  Mars, 
Jupiter,  Saturn,  Uranus,  and  Neptune.  The  first  six  have  been 
known  from  prehistoric  times.  Uranus  was  discovered  by  Sir  Wil- 
liam Herschel  in  1781,  and  Neptune  was  discovered  by  Galle  in  1846. 

The  planetoids  are  like  the  planets,  whence  their  name,  except 
that  they  are  very  small  and  very  numerous.  Nearly  all  of  them 
revolve  around  the  sun  in  the  region  between  the  orbit  of  Mars  and 
the  orbit  of  Jupiter.  The  comets  and  meteors  are  wandering  mem- 
bers of  the  system  which  pass  around  the  sun  in  elongated  orbits, 
sometimes  going  out  so  far  they  probably  never  return. 

It  is  possible  to  find  the  distances  of  the  planets  in  terms  of  the 
earth's  distance  by  rather  simple  observations.  In  Fig.  66,  let  S 
represent  the  sun,  E  the  earth,  and  V  Venus.  Suppose  Venus  is  at 
its  greatest  apparent  distance  from  the  sun  as  seen  from  the  earth. 
Then  the  angle  at  V  is  a  right  angle.  The  angle  a  is  given  by  the 

Copyright,  1912,  by  American  School  of  Correspondence. 


138 


ASTRONOMY 


Fig.  66.     Finding  the  Relative  Distance  of 

Venus  from  Observations  at  the  Time 

of  Its  Greatest  Elongation 


observations.  The  angle  at  S  is  therefore  known,  since  the  sum  of 
the  interior  angles  of  a  triangle  equals  two  right  angles.  Conse- 
quently, in  the  triangle  ESV  the  angle  at  E  and  the  angle  at  S  are 

known  and  the  included  side  ES 
is  the  distance  from  the  earth  to 
the  sun.  From  this  the  distance 
SV  can  be  computed.  The  prob- 
lem is  a  little  more  difficult  for 
planets  which  are  farther  from 
the  sun  than  the  earth  is,  but  it 
is  solved  in  essentially  the  same 
way. 

Orbits   of   the    Planets.     The 
character   of   the    orbits    of    the 
planets  was  first  found  by  Kepler 
about  1618  by  discussing  partic- 
ularly Tycho  Brahe's  observations 
of  Mars.  The  three  laws  of  planetary  motion  which  he  discovered  are : 
LAW  I.     Every  planet  moves  so  that  the  radius  from  the  sun  to  it 
sweeps  over  equal  areas  in  equal  intervals  of  time,  whatever  their  length. 
LAW  II.     The  orbit  of  every  planet  is  an  ellipse  with  the  sun  at 
one  of  its  foci. 

LAW  III.  The  squares  of  the  periods  of  any  two  planets  are  to 
each  other  as  the  cubes  of  their  respective  mean  distances  from  the  sun. 
To  these  laws,  which  relate  to  the  fundamental  properties 
of  the  motions  of  the  planets,  it  might  be  added  that  the  planes  of 
the  orbits  of  the  planets  are  nearly  coincident  and  that  the  planets 
all  revolve  around  the  sun  in  the  same  direction.  It  is  also  an  impor- 
tant fact  that  the  eccentricities  of  their  orbits  are  in  all  cases  small. 

From  Kepler's  laws  of  motion  Newton  deduced  most  important 
consequences.  He  proved,  in  1686,  that  it  follows  from  the  first  law 
of  motion  that  the  forces  to  which  the  planets  are  subject  are  directed 
toward  the  sun.  Before  this  time  there  was  no  well-established 
connection  between  the  sun  and  the  motions  of  the  planets.  In  fact, 
it  was  generally  supposed  that  there  was  some  force  continually 
urging  the  planets  on  in  their  orbits.  As  a  preliminary  to  this  con- 
clusion Newton  laid  down  the  fundamental  laws  of  motion  given 
above  in  connection  with  the  motions  of  the  earth. 


ASTRONOMY  139 

Newton  also  showed  that  it  follows  from  Law  II  that  the  forces 
to  which  the  planets  are  subject  vary  inversely  as  the  squares  of 
their  distances  from  the  sun.  He  proved  in  this  connection  that  if 
this  is  the  law  of  force  the  elliptical  orbits  are  not  the  only  ones 
possible.  It  is  equally  possible  for  a  body  to  move  subject  to  the 
law  of  gravitation  in  a  parabola  or  a  hyperbola.  These  curves  are 
similar  in  many  respects  to  the  ellipse. 

In  Fig.  67  let  S  represent  the  sun  and  E  an  ellipse  with  one  of 
its  foci  at  S.    If  the  point  A  on  the  ellipse  is  kept  fixed  and  the  one 
focus  remains  at  S,  and  if  the  other  end  of 
the  ellipse   is  moved  away  to  the  right  to 
infinity,  then  the  ellipse  becomes  the  curve 
P,  which  is  a  parabola.    A  parabola  has  but 
one  focus.    The  two  arms  of  the  parabola  are 
more  nearly  parallel  as  the  distance  to  the 
right  increases,  and  approach  exact  parallelism 
as  the  distance  to  the  right  approaches  infinity.       Fig-  67;taJ0aJbits  Plan" 
If  the  arms  of  the  parabola  are  opened  out  so 
that  they  are  no  longer  ultimately  parallel,  we  get  the  hyperbola  H. 

Some  of  the  comets  move  in  parabolas  and  possibly  a  few  in 
hyperbolic  orbits.  It  follows  that  they  also  move  around  the  sun 
in  obedience  to  the  law  of  gravitation. 

It  follows  from  Kepler's  third  law  that  if  all  the  planets  were 
at  the  same  distance  from  the  sun  they  would  be  attracted  by  it 
the  same  per  unit  mass.  This  result  is  by  no  means  self-evident. 
For  example,  the  sun  might  attract  different  kinds  of  matter  differ- 
ently; and  if  so  it  would  attract  the  planets  differently  if  they  were 
all  at  the  same  distance  unless  they  were  made  of  precisely  the  same 
materials  in  the  same  proportions.  Since  it  is  improbable  that  their 
different  substances  are  in  exactly  the  same  proportion,  it  is  improb- 
able that,  if  gravitation  were  selective,  they  would  all  be  attracted  by 
the  same  amount  if  they  were  at  the  same  distance. 

Law  of  Gravitation.  The  law  of  gravitation  is  one  of  the  greatest 
and  most  far-reaching  discoveries  ever  made  in  science.  Stated  in 
its  generality  it  is  this: 

Every  particle  of  matter  in  the  universe  attracts  every  other  par- 
ticle with  a  force  which  is  proportional  to  the  product  of  their  masses 
and  which  varies  inversely  as  the  squares  of  their  distances  apart. 


140  ASTRONOMY 

It  relates  every  particle  in  the  universe  to  every  other  par- 
ticle. If  the  position  of  any  mass  in  the  whole  universe  changes, 
the  force  which  it  exerts  on  every  other  particle  in  the  universe  is 
changed  because,  according  to  the  law,  force  depends  upon  the 
distance.  If  a  person  moves,  the  gravitative  force  reaching  out 
from  him  to  the  two  farthest  bodies  is  changed.  If,  as  is  now 
believed,  every  mental  activity  is  accompanied  by  a  physical  change 
in  the  brain,  then  every  thought  is  accompanied  by  a  change  of 
gravitative  force  throughout  the  universe.  Of  course,  these  changes 
are  exceedingly  minute  and  may  be  for  all  practical  purposes  entirely 
neglected.  The  point  of  interest  here  is  the  fact  of  their  existence. 

More  immediate  and  important  consequences  of  the  law  of 
gravitation  are  the  motions  of  the  heavenly  bodies  and  their  influences 
upon  one  another.  After  the  law  was  once  discovered  it  became  an 
instrument  for  further  discoveries.  Time  after  time  mathematicians 
have  predicted,  on  the  basis  of  the  law  of  gravitation,  things  which 
ought  to  be  observed  and  have  told  the  observers  when  and  where 
to  look  for  them.  The  exactness  of  the  law  of  gravitation  is  shown 
by  the  fact  that  their  predictions  have  always  been  verified.  No 
other  law  in  all  the  realm  of  science  is  subject  to  such  delicate  tests 
and  is  proved  with  so  high  a  degree  of  certainty.  It  is  for  this  reason 
that  it  is  used  with  such  confidence  in  arriving  at  results  which  can 
never  be  reached  by  direct  processes.  For  example,  in  the  study  of 
the  interior  of  the  earth  it  was  inferred  from  the  nature  of  the  changes 
produced  in  the  rotation  of  the  earth  by  the  attraction  of  the  moon 
and  sun  on  its  equatorial  bulge,  that  its  interior  is  on  an  average  very 
rigid.  This  result  is  no  more  certain  than  the  laws  and  the  obser- 
vations upon  which  it  is  based.  The  observations  are  subject  in  this 
case  to  no  serious  error,  and  our  confidence  in  the  conclusion  is  grea^t 
because  of  its  being  based  upon  the  fundamental  law  of  gravitation. 

The  law  of  gravitation  was  the  most  important  discovery  of 
Sir  Isaac  Newton,  one  of  the  greatest  men  the  world  has  produced. 
In  Westminster  Abbey  where  England  buries  the  members  of  its 
royal  family  and  the  great  men  it  has  produced,  there  is  a  tablet 
erected  in  honor  of  the  memory  of  Newton  on  which  is  an  inscription 
in  Latin  which  translated  reads:  "Mortals,  congratulate  yourselves 
that  so  great  a  man  has  lived  for  the  honor  of  the  human  race." 
This  splendid  tribute  scarcely  surpasses  those  expressions  of  esteem 


ASTRONOMY  141 

made  by  the  foremost  scholars  of  the  world  who  have  worked  in  the 
same  line.  The  brilliant  German,  Leibnitz,  who  was  a  contemporary 
and  in  some  respects  a  rival  of  Newton,  said:  'Taking  mathematics 
from  the  beginning  of  the  world  to  the  time  when  Newton  lived, 
what  he  had  done  was  much  the  better  half."  The  French  mathe- 
matician, LaGrange,  who  was  one  of  the  greatest  masters  of  celestial 
mechanics,  said:  "Newton  was  the  greatest  genius  that  ever  existed, 
and  the  most  fortunate,  for  we  cannot  find  more  than  once  a  system 
of  the  world."  The  English  scientist,  Whewell,  wrote  in  his  "History 
of  Inductive  Science" :  "It  (the  law  of  gravitation)  is  indisputably 
and  incomparably  the  greatest  scientific  discovery  ever  made 
whether  we  look  at  the  advance  which  it  involved,  or  the  extent  of 
the  truth  disclosed,  or  the  fundamental  and  satisfactory  nature  of 
this  truth." 

Newton,  with  the  humility  characteristic  of  great  minds  who 
see  how  little  they  know  compared  with  that  which  they  do  not 
know  but  would  like  to  understand,  said:  "I  do  not  know  what  I 
may  appear  to  the  world;  but  to  myself  I  seem  to  have  been  only 
like  a  boy  playing  on  the  seashore  and  diverting  myself  in  now 
and  then  finding  a  smoother  pebble  or  a  prettier  shell  than  the  ordi- 
nary, whilst  the  great  ocean  of  truth  lay  undiscovered  before  me." 

One  of  the  satisfactory  things  in  science  is  that  in  it  are  dis- 
covered fundamental  laws  such  as  the  law  of  gravitation.  It  satisfies 
our  instincts  for  absolute  truth. 

Distances  of  the  Planets.  The  mean  distances  of  the  planets 
from  the  sun,  which  means  half  of  the  lengths  of  their  orbits,  are: 

Mercury 36,000,000  miles 

Venus 67,200,000  miles 

Earth 92,900,000  miles 

Mars 141,500,000  miles 

Jupiter 483,300,000  miles 

Saturn 886,000,000  miles 

Uranus 1,781,900,000  miles 

Neptune 2,791,600,000  miles 

The  diameter  of  the  sun  is  about  866,000  miles. 

The  figures  which  have  been  given  represent  so  vast  distances, 
and  cover  so  wide  a  range,  that  it  is  difficult  to  form  any  adequate 
mental  picture  from  them.  The  relative  dimensions  of  the  system 
can  be  shown  better  by  means  of  a.  diagram  than  by  the  numbers. 


142 


ASTRONOMY 


Suppose,  for  example,  we  should  draw  a  map  of  the  system,  taking 
for  the  orbit  of  Mercury  a  circle  one  inch  in  diameter.  On  this  scale 
the  sun  would  be  represented  by  a  circle  ^V  of  an  inch  in  diameter, 
and  the  earth  by  an  invisible  dot,  scarcely  more  than  yinnr  of  an  inch 
across.  On  the  same  scale  the  distance  from  the  sun  to  Neptune 
would  be  a  little  over  three  feet.  Consequently,  it  is  not  possible  to 
put  such  a  picture  on  the  printed  page.  If  we  should  represent  the 
orbit  of  Neptune  by  a  circle  four  inches  in  diameter,  which  is  about 
as  large  as  can  be  put  on  the  page,  the  orbit  of  Mercury  would  be 
about  -fa  of  an  inch  in  diameter.  Obviously,  then,  it  is  impossible  on 
the  printed  page  to  give  a  diagram  showing  the  whole  system  to 
scale.  However,  this  should  not  deter  the  reader  from  making  such 

a  diagram  on  a  suitable  place  as, 
for  example,  on  a  blackboard  or 
a  very  large  sheet  of  paper. 

Certain  features  of  the  system 
can,  however,  be  brought  out  by 
means  of  the  diagrams.  Fig.  68 
shows  the  orbits  of  the  four  plan- 
ets nearest  the  sun  to  relative 
scale.  It  is  apparent  from  the 
figure  that  they  are  spaced  with 
a  considerable  degree  of  regu- 
larity. 

Fig.  68.     The  Orbits  of  the  Terrestrial  Fig.  69  shoWS  the  Orbits  of  the 

planets  beginning  with  Mars  and 

ending  with  Neptune.  Now  it  is  possible  to  imagine  the  orbits  of  the 
three  planets  which  are  nearer  the  sun  than  Mars  inside  the  small 
circle  which  represents  its  orbit.  From  this  diagram  it  is  evident 
that  the  farthest  planets  are  spread  out  at  enormous  distances. 
The  space  between  the  orbits  of  Jupiter  and  Saturn  is  much  greater 
than  all  that  interior  to  the  orbit  of  Jupiter;  and  that  between  the 
orbits  of  Saturn  and  Uranus  is  greater  than  all  of  that  interior  to  the 
orbit  of  Saturn;  and  similarly  for  the  orbits  of  Uranus  and  Neptune. 
The  apparent  diameters  of  the  sun,  as  seen  from  the  different 
planets,  are  inversely  as  their  distances  from  the  sun.  The  sun  as 
seen  from  the  earth  has  an  apparent  diameter  of  a  little  over  half 
a  degree.  As  seen  from  Mercury  its  apparent  diameter  is  nearly 


ASTRONOMY 


143 


three  times  this.  Its  apparent  area,  which  varies  as  the  square  of 
its  apparent  diameter,  is  consequently  nearly  nine  times  as  great  as 
seen  from  Mercury  as  it  is  as  seen  from  the  earth.  Considering  the 
other  extreme  we  find,  since  Neptune  is  30  times  as  far  from  the  sun 
as  the  earth  is,  that  the  apparent  diameter  of  the  sun  as  seen  from 
Neptune  is  only  one  minute  of  arc.  Now,  a  body  whose  apparent 


Fig.  69.     The  Orbits  of  the  Major  Planets  to  the  Same  Scale 

diameter  is  less  than  one  minute  appears  to  the  unaided  eye  like  a 
point  of  light.  Therefore,  as  seen  from  Neptune,  the  sun  would 
appear  like  a  star,  only  immensely  brighter  than  any  star  in  our  sky. 
Its  apparent  area  as  seen  from  Neptune  would  be  T&IF  that  as  seen 
from  the  earth.  Consequently,  the  amount  of  light  and  heat  received 
on  Neptune  per  unit  area  is  ^fo  that  received  by  the  earth.  One 
is  apt  to  draw  the  erroneous  conclusion  that  Neptune  is  a  rather  dark 
place.  But  when  we  reflect  that  moonlight  is  equal  to  only 


144 


ASTRONOMY 


TABLE  IV 
Planets  in  Order  from  Sun  with  Apparent  and  Actual  Diameters 


Planet 

Greatest  Apparent  Diameter 
(seconds  of  arc) 

=; 

Diameter 
(miles)                         | 

Mercury 

13. 

2,765 

Venus 

67. 

7,826 

Earth 

7,913 

Mars 

25. 

(  4,352  (equatorial) 
I  4,312  (polar) 

Jupiter 

50. 

f  90,  190  (equatorial) 
184,570  (polar) 

Saturn 

20. 

(76,470  (equatorial) 
169,780  (polar) 

Uranus 

49. 

34,900 

Neptune 

21. 

32,900 

of  sunlight,  while  the  illumination  of  Neptune  is  only  -g-J-g-  that  of 
the  earth,  it  is  seen  that  sunlight  on  Neptune  is  really  an  intense 
illumination,  being  about  700  times  full  moonlight  here  on  the  earth. 

The  climate  of  a  planet  depends  to  a  large  extent  upon  the 
amount  of  light  and  heat  it  receives  from  the  sun.  Other  things  being 
equal,  particularly  the  constitution  of  the  atmosphere  and  the  radia- 
tion, the  climate  of  Mercury  would  be  the  hottest  of  all  the  planets, 
and  that  of  Neptune  the  coldest.  Since  Neptune  receives  so  small  an 
amount  of  heat  and  light  compared  to  the  earth,  it  is  clear  that  unless 
its  atmosphere  is  peculiarly  adapted  to  preserving  a  high  temperature 
or  unless  the  planet  is  still  hot  itself,  its  surface  must  be  very  frigid. 

Dimensions  and  Masses  of  Planets.  The  diameters  of  the  plan- 
ets differ  almost  as  much  as  their  distances  from  the  sun.  In  a 
general  way  those  which  are  near  the  sun  are  small,  and  those  which 
are  far  away  are  large.  Their  actual  sizes  are  found  from  measure- 
ments of  their  apparent  diameters  after  their  distances  are  known. 
Table  IV,  based  on  measurements  by  Barnard  at  the  Lick  Observa- 
tory, gives  the  planets  in  their  order  from  the  sun,  in  the  second 
column  their  greatest  apparent  diameters  as  seen  from  the  earth, 
and  in  the  third  column  their  actual  diameters  in  miles. 

The  circles  of  Fig.  70  show  better  than  these  numbers  the  rela- 
tive dimensions  of  the  planets.  The  striking  thing  is  the  smallness 
of  the  earth  with  respect  to  the  great  planets. 

Since  the  surfaces  of  similar  bodies  are  as  the  squares  of  their 
like  dimensions  and  the  volumes  as  the  cubes  of  their  like  dimen- 


ASTRONOMY 


145 


TABLE  V 
Surface  and  Volume  of  Planets  as  Compared  to  Earth 


Planet 

Surface 

Volume 

Planet 

Surface 

Volume 

Mercury 
Venus 
Earth 
Mars 

0.12 
0.98 
1.00 
0.30 

0.04 
0.97 
1.00 
0.16 

Jupiter 
Saturn 
Uranus 
Neptune 

122.0 
85.6 
19.5 
17.3 

1,350.0 
790.0 

85.8 
71.9 

sions,  it  follows  that  the  differences  in  surfaces  and  volumes  of  the 
planets  are  much  greater  than  the  differences  in  their  diameters. 

Table  V  gives  the  comparison  taking  the  surface  and  volume 
of  the  earth  as  a  unit. 

JUPITCR 


O 

MERCURY 


O 

vtnus 

o 

EARTH 


o 

MARS 


Fig.  70.     The  Planets  Drawn  *to  the  Same  Scale 

The  masses  of  the  planets  depend  upon  their  size  and  upon  their 
density.  The  masses  of  those  that  have  satellites  are  found  by  the 
time  it  takes  their  satellites  to  revolve  around  them.  It  is  easy  to 
see  that  the  greater  the  mass  of  planet  the  shorter  will  be  the  period 
of  the  satellite  at  a  given  distance.  The  formula  relating  their  period, 
the  distance,  and  the  mass  of  the  planet,  is  one  which  is  derived 
from  the  law  of  gravitation  and  is  given  in  celestial  mechanics.  It  is 


146 


ASTRONOMY 


TABLE  VI 
Masses  and  Densities  of  Sun  and  Planets 


Object 

Mass  (Earth  =1) 

Mass  (Sun=l) 

Density  (  Water  =1) 

Sun 

332,000.0 

1 

1.41 

Mercury 

0.033 

serins  IT 

3.70 

Venus  ' 

0.82 

iWinnr 

4.89 

Earth 

1.0 

raaVrnr 

5.53 

Mars 

0.11 

TT5*Otftfff 

3.95 

Jupiter 

317.7 

lo^y 

1.53 

Saturn 

94.8 

rare 

0.72 

Uranus 

14.6 

TSZ^STJ 

1.22 

Neptune 

17.0 

T¥ffOO 

1.11 

where  P  is  the  period  expressed  in  days,  a  the  distance  from  the 
satellite  to  the  planet  expressed  in  terms  of  the  earth's  distance  from 
the  sun,  k  a  constant  which  equals  about  -gV,  M  the  mass  of  the 
planet,  and  m  the  mass  of  the  satellite. 

The  masses  of  those  planets  which  do  not  have  satellites  are 
found  from  their  attractions  for  one  another,  and  for  comets  which 
pass  near  them.  The  planets  are  so  far  apart  and  they  are  so  small 
compared  to  the  sun  that  their  mutual  attractions  are  not  large 
enough  to  enable  us  to  determine  their  masses  very  accurately. 
When  comets  pass  near  them  more  exact  results  can  be  secured,  but 
the  best  that  can  be  obtained  in  this  way  is  very  much  less  accurate 
than  those  furnished  by  the  periods  of  the  satellites. 

Since  the  diameters  of  most  of  the  planets  are  known  and  their 
masses  are  found  as  has  just  been  explained,  it  is  possible  to  determine 
their  densities  by  dividing  the  masses  by  the  volumes.  Table  VI 
gives  the  results  for  the  sun  and  the  planets.  In  the  second  column 
the  mass  of  the  earth  is  taken  as  the  unit,  and  the  masses  of  the 
other  members  of  the  system  are  expressed  in  terms  of  it.  In  the 
third  column  the  mass  of  the  sun  is  taken  as  the  unit;  and  in  the 
fourth  column  the  densities  of-  all  these  bodies  are  given,  taking 
water  as  the  standard. 

It  is  seen  from  Table  VI  that  Jupiter  is  not  only  much  larger 
than  any  other  planet,  but  its  mass  is  more  than  three  times  that  of 
any  other  planet  and  about  two  and  a  half  times  that  of  all  the  other 
planets  combined.  It  is  also  observed  that  the  earth  is  the  densest 


ASTRONOMY 


147 


TABLE   VII 
Comparative  Surface  Gravity  of  Sun  and  Planets 


Object 

Surface  Gravity 

Object 

Surface  Gravity 

Sun 

27.7 

Jupiter 

2.61 

Mercury 

0.38 

Saturn 

1.19 

Venus 

0.86 

Uranus 

0.88 

Earth 

1.00 

Neptune 

0.88 

Mars 

0.38 

member  of  the  solar  system.     The  rarest  one  is  the  planet  Saturn, 
whose  mean  density  is  about  .three-fourths  that  of  water. 

The  surface  gravity,  or  the  relative  weight  of  an  object  on  the 
surface  of  a  planet,  depends  upon  its  mass  and  dimensions.  Accord- 
ing to  the  law  of  gravitation  the  weight,  which  is  a  consequence  of 
the  attraction,  is  directly  proportional  to  the  mass  of  the  planet  and 
inversely  proportional  to  the  square  of  the  distance  from  its  surface 
to  its  center.  From  this  law  and  the  preceding  tables  Table  VII 
has  been  computed . 

It  is  seen  from  Table  VII  that  although  the  earth  has  a  greater 
density  than  any  other  member  of  the  system,  its  surface  gravity  is  con- 
siderably less  than  that  of  Jupiter  and  the  sun.  In  the  case  of  Saturn 
its  larger  mass  is  almost  exactly 
offset  by  its  greater  diameter. 

Periods  of  the  Planets.  The 
periods  of  the  planets  depend 
upon  their  distances  from  the 
sun,  the  greater  the  distances  the 
longer  the  period.  In  fact,  the 
formula  for  determining  the  peri- 
ods is  given  in  the  preceding 
article,  where  M  in  the  present 
case  must  be  taken  to  represent 
the  mass  of  the  sun  and  m  the 
mass  of  the  planet.  The  period 
referred  to  in  the  present  connection  is  the  time  it  takes  a  planet 
to  revolve  around  the  sun  as  observed  from  the  sun.  This  is  called 
the  sidereal  period.  There  is  another  period  which  is  more  im- 
portant for  observational  purposes  known  as  the  synodic  period. 


Fig.  71.    Definition  of  the  Synodic  Period 


148 


ASTRONOMY 


In  Fig.  71,  let  S  represent  the  sun,  and  the  two  circles  the  orbits 
of  Venus  and  the  earth,  respectively.  Suppose  at  a  certain  time  the 
sun,  Venus,  and  the  earth  are  in  a  straight  line  at  SV^^  Suppose 
the  directions  of  motion  are  indicated  by  the  arrows  in  the  diagram. 
Venus  moves  faster  than  the  earth  both  in  miles  per  second  and  in 
angle;  consequently,  the  line  from  S  to  V  will  move  on  ahead  of  the 
line  from  S  to  E,  and  after  a  time  will  gain  a  revolution  on  it.  Let 
us  suppose  that  by  the  time  the  earth  gets  around  to  E2  Venus  will 
have  gone  around  its  orbit  back  to  Vif  and  on  the  second  time  around 
up  to  V2,  so  that  it  is  again  in  a  line  with  the  earth.  It  will  be  seen 
by  an  examination  of  the  diagram  that,  under  the  hypotheses,  the 


Fig.  72.     Venus  at  Greatest  Elongation 


Fig.  73.     The  Planet  Mars  in  Opposition 


earth,  Venus,  and  the  sun  have  not  been  in  a  straight  line  since  they 
were  at  SV^Ei.  This  period  from  a  certain  relative  position  to  the 
same  relative  position  again  is  called  the  synodic  period. 

Instead  of  supposing  that  the  earth,  Venus,  and  the  sun  are 
initially  in  a  straight  line,  we  might  start  from  the  time  Venus  seems 
to  be  farthest  from  the  sun,  as  indicated  in  Fig.  72,  with  the  earth  at 
E1  and  Venus  at  Kx.  In  this  case  when  the  earth  gets  to  E2,  Venus 
will  be  at  F2  and  will  again  be  at  its  apparent  greatest  distance  from 
the  sun.  This  is  also  a  synodic  period  and  exactly  equal  to  the  pre- 
ceding. When  the  earth,  Venus,  and  the  sun  are  located  relatively 
to  each  other,  as  indicated  in  Fig.  72,  Venus  is  in  the  position  best 
observable  from  the  earth.  If  the  planet  were  farther  from  the  sun 
than  the  earth  is,  the  straight  line  situation,  indicated  in  Fig.  71, 
would  be  the  time  when  observations  could  be  most  advantageously 


ASTRONOMY  149 

made.  When  the  relations  are  as  indicated  in  Fig.  72,  the  planet  is 
said  to  be  in  greatest  elongation.  That  is,  as  it  is  observed  from  the 
earth  it  is  farthest  out  from  the  sun.  When  the  situation  is  as 
indicated  in  Fig.  71,  the  planet  is  said  to  be  in  conjunction  with  the 
sun.  In  Fig.  73,  which  shows  the  orbit  of  the  earth  and  Mars,  the 
planet  is  said  to  be  in  opposition  when  the  relations  of  the  bodies  are 
as  indicated  in  the  diagram.  In  observing  a  planet  which  is  farther 
from  the  sun  than  the  earth,  obviously  the  most  convenient  time 
for  observations  is  when  it  is  in  opposition,  for  then  it  is  nearest  to 
the  earth  and  the  illuminated  side  is  toward  the  earth 

It  is  obvious  from  Fig.  72  that  a  planet  which  is  nearer  the  sun 
than  the  earth,  can  have  an  elongation  either  side  of  the  sun.     If  the 
planet  is  to  be  observed  in  the  evening,  which  means  that  it  must  be 
above  the  horizon  after  the  sun 
has  set,  it  must  be  east  of  the 
sun.     Since  the  evening  is  in  gen- 
eral a  more  convenient  time  for 
observation  than  the  early  morn- 
ing, we  shall  make  our  calcula- 
tions for  the  eastward  elongation. 
Since  the   earth   rotates   in   the 
same  direction  that  it  goes  around 
the  sun,  viz,  from  west  to  east, 
it  follows  that  Venus  has  a  west- 
ward elongation   when  its  rela-      Fig  74    The  Motions  of  Venus  Eastward 
tions  to   the  sun  and  the  earth 

are  as  indicated  in  Fig.  72.  This  can  be  seen  by  following  a  point 
on  the  earth  in  its  daily  rotation.  The  point  will  pass  under  Venus, 
i.  e.,  Venus  will  apparently  cross  its  meridian,  before  it  passes  under 
the  sun,  and  consequently  Venus  will  set  before  the  sun  does. 

Suppose  Venus  has  its  greatest  eastward  elongation  and  consider 
Fig.  74.  When  Venus  is  in  the  position  F2,  it  has  its  greatest  eastern 
elongation.  Suppose  for  simplicity  that  the  earth  stands  still  while 
Venus  moves  forward  in  its  orbit.  It  will  pass  between  the  earth  and 
the  sun  and  arrive  at  its  greatest  westward  elongation  at  Vi.  Then 
it  passes  apparently  back  across  the  sun  on  the  side  of  the  sun  oppo- 
site to  the  earth  and  arrives  again  at  F2.  It  is  clear  from  the  dia- 
gram that  the  time  from  F2  to  V1}  i.  e.,  from  eastward  elongation  to 


150 


ASTRONOMY 


TABLE  V11I 

* 

Data  from  Which  to  Compute  Times  Favorable  for  Observation  of  Planets 


Planet 

Sidereal  Period 
(Years) 

Synodical  Period 
(Years) 

Date  of  Eastern  Elon- 
gation or  of  Opposition 

Mercury 
Venus 
Earth 
Mars 

0  24 
0.62 
1.00 

1.88 

0.32 
1.63 

July    24,  1912 
July      6,  1911 

2.136 

Nov.  24,  1911 

Jupiter 
Saturn 

11.86 
29.46 

1.092 
1.035 

May  31,  1912 
Nov.  22,  1912 

Uranus 
Neptune 

84.02 
164.78 

1.012 
1.006 

July  24,  1912 
Jan.    13,  1912 

westward  elongation  is  longer  than  the  time  from  V1  to  V2.  The 
same  thing  is  true  when  the  earth  moves  forward  in  its  orbit.  And 
similar  statements  are  true  for  the  planet  Mercury  whose  orbit  is 
also  inferior  to  that  of  the  earth.  Since  the  orbit  of  Mercury  is 
smaller,  these  differences  just  mentioned  in  the  time  of  passage  from 
one  elongation  to  the  other  are  less  than  in  the  case  of  Venus. 

The  planets  which  are  nearer  the  sun  than  the  earth  are  called 
inferior  planets,  and  those  which  are  farther  from  the  sun,  superior 
planets.  Suppose  an  inferior  planet  is  observed  at  its  greatest  eastern 
elongation.  The  question  is  when  will  it  again  be  in  that  favorable 
position  for  observation.  This  is  its  synodical  period.  It  can  be 
determined  by  observations,  or  it  can  be  computed  without  difficulty 
from  the  sidereal  period.  In  the  case  of  a  superior  planet  the  time 
for  the  most  favorable  observation  is  in  opposition,  and  after  the 
synodical  period  the  planet  will  have  returned  to  that  relative  posi- 
tion. Hence,  it  follows  that  in  order  to  find  the  time  when  a  planet 
will  be  favorably  situated  for  observations  it  is  necessary  to  know 
once  when  it  was  in  eastern  elongation  if  it  be  an  inferior  planet,  or 
in  opposition  if  it  be  a  superior  planet,  and  then  to  add  enough 
synodical  periods  to  arrive  at  least  to  the  date  of  computation.  For 
example,  suppose  it  were  known  that  Mars  was  in  opposition  in  1900 
on  a  certain  date  and  that  its  synodical  period  was  exactly  two 
years;  and  suppose  in  1911  one  wished  to  know  when  it  would  again 
be  in  opposition.  If  he  added  five  of  the  two-year  periods  it  would 
bring  the  date  forward  to  1910,  which  having  already  passed  by 
would  not  give  the  observer  the  information  he  desired.  But  adding 


ASTRONOMY  151 

six  periods  he  would  find  that  in  1912  on  a  certain  date  Mars  would 
again  be  in  opposition,  and  he  could  be  prepared  to  observe  it.  Of 
course,  in  actual  practice  the  numbers  do  not  come  so  simply  as  in 
the  example. 

Table  VIII  gives  the  sidereal  and  synodical  periods  of  the 
planets,  dates  of  great  eastern  elongations  in  the  case  of  the  inferior 
planets,  and  of  opposition  in  the  case  of  the  superior  planets. 
From  these  dates  and  the  synodical  periods  the  times  favorable  for 
observations  of  the  planets  can  be  determined  for  as  long  a  period 
as  is  desired. 

The  Two  Groups  of  Planets.  It  is  evident  from  the  preceding 
data,  which  give  a  general  idea  of  the  solar  system  considered  as  a 
whole,  that  the  planets  naturally  fall  into  two  groups  which  are 
distinct  in  many  of  their  characteristics.  The  first  group  comprises 
Mercury,  Venus,  Earth,  and  Mars,  and  is  called  the  terrestrial  group 
from  the  general  similarity  of  these  bodies  to  the  earth.  Jupiter, 
Saturn,  Uranus,  and  Neptune  constitute  the  other  group,  called  the 
major  planets  because  of  their  relatively  great  size.  The  distinction 
in  the  two  groups  is  seen  from  the  fact  that  the  major  planets  are  on 
the  average  17.6  times  as  far  from  the  sun  as  the  terrestrial  planets. 
On  the  average  the  terrestrial  planets  receive  per  unit  area  310  times 
i  as  much  heat  and  light  from  the  sun  as  the  major  planets.  On  the 
average  the  diameter,  surfaces,  and  volumes  of  the  major  planets  are 
10,  100,  and  1,000  times  greater  than  those  of  the  terrestrial  planets. 
The  masses  of  the  major  planets  average  224  times  those  of  the 
terrestrial  planets,  while  their  densities  are  only  a  little  over  one-fifth 
as  great.  The  periods  of  revolution  of  the  major  planets  average 
77.6  times  those  of  the  terrestrial  group  and,  as  we  shall  see,  their 
periods  of  rotation  so  far  as  they  are  known  average  less  than  one- 
half  of  those  of  the  terrestrial  planets.  These  facts  are  sufficient  to 
establish  the  grouping  of  the  planets  which  has  been  adopted. 

Notwithstanding  the  diversities  among  the  members  of  the  two 
groups  of  planets,  there  are  many  harmonies  among  all  of  them 
considered  together.  The  harmonies  are  fully  as  important  as  the  di- 
versities. The  foremost  of  the  harmonies  to  be  noted  is  that  the 
planets  and  more  than  700  known  planetoids  all  revolve  around  the 
sun  in  the  same  direction  and  nearly  in  the  same  plane.  The  greatest 
divergencies  from  the  plane  of  motion  are  in  the  case  of  the  planetoids. 


152  ASTRONOMY 

The  sun  rotates  in  the  same  direction  and,  indeed,  so  do  all  the 
planets  whose  rotations  are  known.  The  moon  revolves  around  the 
earth  in  the  same  direction  and  rotates  in  this  direction.  In  fact, 
the  satellites  of  all  the  planets  except  one  each  of  Jupiter  and  Saturn, 
and  the  satellites  of  Uranus  and  Neptune,  revolve  in  this  same  direc- 
tion. All  the  orbits  are  very  nearly  circular.  Often  this  does  not 
strike  one  as  being  a  fact  of  any  significance,  but  when  it  is  remem- 
bered that  it  is  just  as  natural  for  the  orbit  of  a  body  moving  subject  to 
the  law  of  gravitation  to  have  any  eccentricity,  it  does,  indeed,  seem  to 
be  a  remarkable  fact.  It  is  as  remarkable  as  it  would  be  if  one  were  to 
find  the  trees  in  a  natural  forest  all  arranged  in  definite  straight  lines. 
The  Planetoids.  If  the  distances  of  the  planets  from  the  sun 
are  examined,  it  will  be  found  that  each  one  is  approximately  twice 
that  of  the  preceding  one  with  the  exception  of  Jupiter,  whose  dis- 
tance is  about  3.5  times  that  of  Mars.  A  more  exact  method  of 
finding  the  relative  distances  is  to  take  the  numbers  0,  3,  6,  12,  24, 
48,  and  so  on,  and  to  add  to  each  of  them  4.  The  sums  thus  obtained 
are  very  nearly  proportional  to  the  distances  of  the  planets  from  the 
sun,  with  the  exception  that  there  is  a  number  falling  between  the 
distance  of  Mars  and  Jupiter.  This  arrangement  of  numbers,  known 
as  "Bode's  Law,"  though  it  was  discovered  by  Titius,  led  astronomers 
at  the  end  of  the  eighteenth  century  to  suspect  that  another  planet 
existed  between  the  orbit  of  Mars  and  that  of  Jupiter.  Bode's  law 
is  not  a  law  in  the  same  sense  that  the  law  of  gravitation  is,  for  it 
expresses  the  facts  only  roughly,  and  no  actual  connection  between 
them  and  it  has  ever  been  established.  However,  it  was  enough  to 
direct  inquiry  toward  the  existence  of  an  unknown  world.  In  1800 
a  number  of  German  astronomers  founded  an  association  whose 
purpose  was  to  search  for  the  unknown  planet.  The  difficulty  in  a 
problem  of  this  sort  arises  from  the  fact  that  a  small  planet  does 
not  look  materially  different  from  a  star,  and  it  is  necessary  to  find 
in  some  way  whether  the  object  viewed  is  a  star  or  not.  One  way 
of  detecting  it  is  to  find  whether  the  object  moves  relatively  to  the 
stars  or  not.  If  so,  it  is  not  a  star.  Consequently,  one  way  to  find 
whether  there  are  any  worlds  undiscovered  is  to  make  a  map  of  all 
the  objects  visible  with  the  instruments  in  use,  and  then  at  a  later 
date  to  see  whether  they  have  the  same  positions  or  not.  While  the 
discussion  of  the  astronomers  was  going  on,  and  while  they  were 


ASTRONOMY  153 

making  preparations  to  carry  out  extensive  observations  in  the  search, 
the  philosopher  Hegel  proved,  or  at  least  claimed  to  have  proved,  by 
the  "most  conclusive  reasoning,"  that  there  were  no  unknown  planets, 
and  remarked  on  the  folly  of  searching  for  them.  Before  the  German 
astronomers  actually  got  to  work,  and  indeed  shortly  before  the 
publication  of  Hegel's  dissertation,  an  Italian  astronomer,  Piazzi, 
at  Palermo,  discovered  an  unknown  world  January  1,  1801,  on  the 
first  day  of  the  nineteenth  century.  He  named  it  Ceres  after  the 
tutelary  goddess  of  Italy. 

In  1801,  communication  was  slow  compared  to  that  which  we 
have  at  the  present  time.  The  news  of  the  discovery  of  Piazzi  did 
not  reach  Germany  until  the  following  spring  and  by  that  time  the 
sun  had  passed  between  the  earth  and  the  planet  and  the  latter  was 
lost  to  view.  Up  to  that  time  it  was  not  known  how  to  compute  an 
accurate  orbit  of  a  planet  from  a  few  observations.  The  problem  of 
getting  the  orbit  of  Ceres  and  the  rediscovery  of  it  led  a  brilliant 
young  German  mathematician  by  the  name  of  Gauss  to  develop  a 
method  for  doing  it.  In  accordance  with  his  computations,  which 
directed  observers  where  to  look  in  the  sky  to  find  this  world,  it  was 
again  picked  up.  It  was  found  upon  examination  and  measurement 
that  its  orbit  was  between  that  of  Mars  and  Jupiter,  at  about  the 
distance  Bode's  law  would  lead  one  to  expect  an  unknown  world  to 
be  found.  The  new  planet  was  surprisingly  small.  According  to 
recent  measurements  of  Barnard  its  diameter  is  485  miles. 

In  March,  1802,  Olbers  discovered  a  second  planetoid  which  he 
named  Pallas,  and  in  September,  1804,  Harding  found  a  third  which 
he  called  Juno.  Olbers  discovered  again  another  in  March,  1807, 
which  is  known  as  Vesta.  After  the  second  planetoid  was  discovered 
it  was  supposed  that  perhaps  they  were  the  fragments  of  some  larger 
planet  which  for  some  unknown  reason  had  exploded.  If  we  imagine 
a  planet  going  around  the  sun  and  exploding  at  some  point  in  its 
orbit,  after  the  explosion  the  fragments  will  go  on  their  way  around 
the  sun  in  distinct  elliptical  orbits.  But  since  all  elliptical  orbits  are 
closed  they  will  all  return  to  the  point  where  the  explosion  took  place. 
The  period  of  a  planet  depends  upon  the  length  of  its  orbit,  and  as 
the  different  fragments  might  move  in  orbits  having  different  lengths 
they  would  not  all  return  to  the  point  of  the  explosion  at  the  same 
time.  If  this  theory  were  correct,  the  position  in  the  sky  to  search 


154 


ASTRONOMY 


for  the  fragments  of  an  exploded  planet  would  be  that  where  they 
cross.  After  two  planets  had  been  discovered  the  computations 
showed  the  two  points  where  their  orbits  intersected,  and  conse- 
quently if  the  explosion  theory  were  correct,  the  other  fragments 
should  be  discovered  some  time  at  one  of  these  two  places.  Since 
this  theory  was  at  first  adopted,  though  it  has  long  been  abandoned, 
the  search  was  prosecuted  most  carefully  in  the  vicinity  of  the  points 
of  intersection  of  the  orbits  of  the  planetoids. 

After  the  discovery  of  the  first  four  planetoids  no  other  one  was 
discovered  until  1845.    This  world  was  picked  up  by  Hencke  after 


Fig.  75.     A  Planetoid  Trail  Photographed  at  the  Yerkes  Observatory 

fifteen  long  years  of  search.  Few  men  would  have  the  patience  to  sit 
at  the  eye  end  of  a  telescope  night  after  night  and  week  after  week 
for  fifteen  years  before  making  a  discovery.  After  1847,  catalogues 
of  the  stars  were  so  extensive  that  it  became  a  relatively  easy 
matter  to  discover  these  objects,  which  were  found  to  be  very  numer- 
ous. But  a  new  epoch  in  their  discovery  began  in  1891  when  Wolf, 
at  Heidelberg,  discovered  one  by  photography.  The  method  is 
extremely  simple.  The  photographic  plate  is  given  a  long  exposure 
in  a  certain  region  with  the  telescope  following  the  stars  so  that 


ASTRONOMY  155 

their  images  come  out  on  the  plate  as  points.  The  planetoids  move 
among  the  stars,  and  if  there  is  one  in  the  field  of  view  its  image  will 
come  out  on  the  plate  as  a  little  streak.  Fig.  75  shows  one  of  these 
photographs  with  a  planetoid  trail  at  the  center  of  the  picture.  These 
little  trails  show  planetoids  and  lead  very  quickly  and  conveniently  to 
their  discovery.  In  some  cases  more  than  one  has  been  found  on  a 
single  plate.  There  are  at  the  present  time  over  700  of  them  known. 

The  old  theory  that  the  planetoids  had  their  origin  in  an  exploded 
planet  has  been  abandoned  because  the  orbits  extend  all  the  way 
from  that  of  Mars  out  to  that  of  Jupiter,  over  a  distance  exceeding 
300,000,000  miles.  The  planetoids  nearest  the  sun  are,  at  their 
nearest  approach  to  those  which  are  near  Jupiter's  orbit,  more  than 
three  times  as  far  from  them  as  the  earth  is  from  the  sun.  In  fact, 
one  was  discovered  in  1898  whose  orbit  is  between  the  orbit  of  the 
earth  and  that  of  Mars,  and  more  recently  others  have  been  discovered 
whose  distances  from  the  sun  are  equal  to  that  of  Jupiter. 

The  first  planetoids  discovered  were  naturally  the  largest  and 
brightest  ones  and  their  diameters  were  from  100  to  500  miles, 
probably  the  latter  figure  being  the  extreme  limit.  Those  of  recent 
discovery  are  much  smaller,  probably  ranging  down  to  approximately 
10  miles  in  diameter.  The  probabilities  are  that  there  are  unlimited 
numbers  of  them  still  smaller.  It  is  impossible  to  determine  their 
mass  since  they  exert  no  appreciable  gravitational  influence  on  other 
known  bodies,  but  if  their  densities  are  comparable  to  those  of  the 
planets,  their  combined  mass  is  probably  not  T^j-  that  of  the  earth. 
If  it  were  greater  than  this  its  attraction  on  Mars  would  sensibly 
disturb  the  orbit  of  this  planet.  Computations  referring  to  these 
planetoids  so  far  discovered,  and  based  on  what  seem  reasonable 
assumptions  regarding  'their  density,  show  that  their  mass  is  less 
than  STTOTF  that  of  the  earth. 

Being  compelled  by  the  observations  to  abandon  the  explosion 
theory  of  their  origin,  one  might  inquire  how  they  have  arisen.  This 
problem  is  wrapped  up  with  that  of  the  origin  of  the  planets.  Appar- 
ently, the  zone  between  the  orbit  of  Mars  and  that  of  Jupiter  was 
one  in  which  there  was  considerable  material,  but  in  which  no  body 
of  dominating  gravitative  influence  existed  to  sweep  up  and  gather 
to  itself  the  widely  scattered  fragments.  We  shall  take  up  again  the 
question  of  the  origin  of  the  planets. 


156  ASTRONOMY 

•The  planetoid  whose  orbit  is  between  that  of  the  earth  and 
Mars,  known  as  Eros,  presented  some  remarkable  peculiarities  to 
astronomers.  In  February  and  March,  1901,  about  three  years  after 
its  discovery,  its  light  began  to  be  variable.  At  its  minimum  it  was 
less  than  one-third  as  bright  as  at  its  maximum,  and  the  period  from 
maximum  to  minimum  was  only  2  hours  and  38  minutes;  or, 
perhaps,  5  hours  and  16  minutes,  composed  of  two  sub-periods  of 
2  hours  and  25  minutes  and  2  hours  and  51  minutes,  respectively. 
In  a  few  months  it  again  was  shining  with  steady  light.  Since  all 
these  bodies  shine  entirely  by  reflected  light,  it  is  difficult  to  account 
for  these  variations.  One  suggestion  for  explaining  them  was  that 
Eros  is  really  composed  of  two  bodies  near  together  which  revolve 
around  their  common  center  of  gravity.  If  this  were  so,  when  the 
bodies  were  in  a  line  with  us  they  would  present  less  surface  than 
when  they  were  sidewise,  and  consequently  would  appear  fainter. 
But  according  to  this  theory  it  is  impossible  to  account  for  so  great 
variations  in  the  light  as  the  observations  actually  show  existed. 

Another  hypothesis  for  the  explanation  of  the  variability  of 
Eros  is  that  the  reflecting  power  on  various  parts  of  it  differs  greatly. 
According  to  this  theory,  when  the  highly  reflective  side  is  toward  us 
it  appears  bright,  and  when  the  duller  side,  darker.  If  this  were  true, 
we  should  have  the  period  of  rotation  from  the  observation  of  the 
changes  in  its  light.  The  chief  difficulty  arises  when  we  attempt  to 
explain  the  large  variability  for  a  time,  and  then  later  the  total 
absence  of  variability.  The  orbit  of  the  planetoid  is  highly  inclined 
to  that  of  the  earth  so  that  we  view  it  under  varying  aspects,  but  in 
spite  of  this  there  are  real  difficulties  in  explaining  the  phenomenon. 

One  of  the  uses  to  which  planetoids  have  been  put  is  to  obtain 
a  very  accurate  measurement  of  the  distance  from  the  earth  to  the 
sun.  The  relative  distances  of  the  planets  can  all  be  found  without 
knowing  any  actual  distance.  In  Fig.  66  it  was  shown  how  the  dis- 
tance from  the  sun  to  Venus  could  be  obtained  in  terms  of  the 
distance  from  the  sun  to  the  earth.  In  a  similar  way  all  the  relative 
distances  in  the  system  can  be  determined.  Then,  if  any  actual 
distance  either  of  a  body  to  the  sun  or  from  one  body  to  another 
can  be  found,  all  the  distances  become  known.  It  is  not  easy  to 
measure  the  distance  from  the  earth  to  the  sun  directly  because  the 
sun  is  a  body  very  poorly  adapted  for  observation.  In  the  first  place, 


ASTRONOMY  157 

it  is  not  a  point  of  light  and,  indeed,  has  no  absolutely  sharp  bound- 
ary. In  the  second  place,  the  light  and  heat  from  it  shining  into 
the  instrument  disturb  the  delicate  adjustments  necessary  for  mak- 
ing accurate  observations.  In  the  third  place,  it  is  very  far  away 
and  the  difficulties  of  obtaining  accuracy  increase  with  the  distance. 
But  the  first  two  objections  to  using  the  sun  as  a  means  of  finding 
the  distances  of  the  members  of  the  solar  system  from  one  another 
are  absent  in  the  case  of  the  planetoids;  and  the  third  is  also  absent 
in  the  case  of  Eros.  Probably  the  most  exact  method  at  the  present 
time  of  finding  the  distances  in  the  solar  system  is  by  measuring  the 
distance  of  Eros.  When  this  planetoid  was  near  to  us  many  observa- 
tions of  its  position,  both  visual  and  photographic,  were  taken. 
Their  reduction  at  many  places,  particularly  at  Cambridge,  Eng- 
land, by  Hincks,  led  to  remarkably  accurate  results  regarding  the 
distance  to  the  sun.  It  must  not  be  supposed  that  our  knowledge 
of  this  distance  depends  upon  this  method  alone,  for  there  are  at 
least  half  a  dozen  others  distinct  from  it.  They  all  agree  in  about 
the  same  distance,  though  some  of  them  give  results  which  have  a 
considerable  degree  of  uncertainty. 

Zodiacal  Light  and  Gegenschein.  The  zodiacal  light  is  a  hazy 
wedge  of  light  stretching  up  from  the  horizon  along  the  ecliptic  just 
as  the  twilight  is  ending  or  the  dawn  beginning.  The  base  of  it  is 
from  20  degrees  to  30  degrees  wide,  and  it  can  be  followed  under 
favorable  atmospheric  conditions,  when  the  moon  is  not  in  the  sky, 
to  a  distance  of  90  degrees  from  the  sun.  Sometimes  a  narrow,  very 
faint  band  of  light  three  or  four  degrees  wide  can  be  traced  entirely 
across  the  sky.  It  is  very  difficult  to  determine  exactly  where  the 
borders  of  the  zodiacal  light  are,  for  it  fades  out  very  gradually  into 
the  darkness  of  the  night  sky,  and  at  its  brightest  is  not  much  brighter 
than  the  Milky  Way. 

The  zodiacal  light  can  best  be  seen  when  the  ecliptic  makes  a 
large  angle  with  the  horizon,  and  this  varies  considerably  at  different 
times  of  the  year.  Suppose  the  sun  is  at  the  vernal  equinox.  It  is 
then  at  the  part  of  its  orbit  where  the  ecliptic  crosses  the  equator 
from  south  to  north.  Suppose  the  sun  is  setting  in  the  western  sky. 
The  equator  comes  up  obliquely  from  the  western  point  on  the 
horizon  and  crosses  the  meridian  at  an  altitude  equal  to  90  degrees 
minus  the  latitude  of  the  observer.  The  ecliptic  comes  up  from  the 


158 


ASTRONOMY 


western  sky  above  the  equator  and  crosses  the  meridian  at  an  altitude 
23.5  degrees  greater  than  that  at  which  the  equator  crosses.  Conse- 
quently it  comes  up  from  the  western  sky  more  nearly  perpendicular 
than  the  equator  does.  Since  the  sun  is  at  the  vernal  equinox  in  the 
spring,  this  is  the  time  of  year  when  the  zodiacal  light  can  best  be  seen 
in  the  evening.  When  the  sun  is  at  the  autumnal  equinox  the  ecliptic 
crosses  the  equator  from  south  to  north  and  comes  up  -from  the 
western  sky  at  sunset  very  obliquely,  being  south  of  the  equator. 
At  this  time  the  zodiacal  light  is  lost  in  the  haze  of  the  horizon  and  is 
not  conspicuous.  If  it  is  desired  to  observe  it  in  the  morning,  then 
it  is  found  by  similar  discussion  that-  the  most  favorable  time  of  the 

year  for  seeing  it  is  in  the  autumn, 
and  the  least  favorable  in  the 
spring. 

The  zodiacal  light  is  probably 
due  to  a  vast  number  of  small 
particles  revolving  around  the  sun 
near  the  plane  of  the  earth's  orbit 
and  extending  out  somewhat  be- 
yond the  path  of  the  earth.  In 
Fig.  76  let  S  represent  the  sun,  E 
the  earth,  and  Z  the  particles  of 
which  the  zodiacal  band  of  mat- 
ter is  composed.  Consider  an  ob- 
server at  0  for  whom  the  sun  has  recently  set.  His  horizon  is  //, 
and  above  H  he  will  see  part  of  the  zodiacal  band  which  is  illuminated 
by  the  sun,  and  it  will  appear  to  him  as  a  hazy  wedge  of  light  in  the 
plane  of  the  earth's  orbit,  that  is,  along  the  ecliptic. 

Die  Gegenschein,  the  German  for  counter-glow,  is  a  very  faint 
oblong  patch  of  light  on  the  ecliptic  precisely  opposite  to  the  sun. 
It  appears  like  an  enlargement  of  the  zodiacal  band.  It  is  so  very 
faint  that  it  can  be  seen  only  under  the  most  favorable  atmospheric 
conditions  and  in  the  absence  of  all  artificial  light.  In  fact,  a  planet 
or  a  bright  star  near  it  is  enough  to  make  it  invisible,  and  the  illumina- 
tion of  the  Milky  Way  is  absolutely  fatal  to  seeing  it.  This  faint 
object  was  not  discovered  until  recent  times  when  it  was  found 
independently  by  three  observers,  Brorsen,  in  1854,  and  later  by 
both  Backhouse  and  Barnard.  One  theory  for  its  explanation  is 


Fig.  76.     The    Zodiacal    Light    Is   Due    to 

Small  Particles  Revolving  around  the  Sun 

near  the  Plane  of  the  Earth's  Orbit 


ASTRONOMY  159 

that  it  is  due  to  a  large  number  of  meteors  circulating  around  a  point 
opposite  to  the  sun  and  about  900,000  miles  from  the  earth.  It 
can  be  shown  mathematically  that  there  is  a  point  in  this  neighbor- 
hood at  which  a  meteor  placed  and  started  suitably  would  always 
stay.  If  one  were  started  near  this  point  there  would  be  a  tendency 
for  it  to  circulate  around  the  point  for  a  time  and  then  to  pass  on. 
A  stream  of  meteors  passing  around  the  sun  and  near  this  point  would 
be  caught  in  a  sort  of  whirlpool  and  would  circulate  around  it  for  a 
time,  and  give  us  just  such  a  faint  illumination  of  the  sky  as  the 
gegenschein  actually  is.  While  this  explanation  seems  very  probable 
we  are  not  absolutely  sure  that  it  is  correct. 

Probably  the  observation  of  the  gegenschein  is  the  best  test 
of  the  power  of  distinguishing  faint  objects.  It  can  not  be  seen 
through  instruments,  because  with  the  telescope  only  a  small  part  of 
the  sky  can  be  observed  and  no  contrast  can  be  obtained.  This 
object  is  from  5  degrees  to  10  degrees  wide  and  10  degrees  to  20 
degrees  long.  The  best  time  for  observing  it  is  in  the  autumn 
months,  September  and  October,  when  there  is  no  moon  in  the  sky. 

Mercury  and  Venus.  Having  discussed  the  solar  system  as  a 
whole  and  the  planets  in  their  relations  to  one  another  and  to  the 
sun,  it  is  in  order  to  consider  them  briefly  as  individuals. 

Mercury  and  Venus,  being  inferior  planets,  are  not  situated  very 
conveniently  for  observations  because  when  they  are  nearest  to  us 
their  dark  sides  are  toward  us.  On  this  account  the  surface  mark- 
ings of  these  bodies  are  not  so  well  known  as  those  of  the  superior 
planets,  some  of  which  are  not  near  the  earth.  Mercury  can  be 
observed  best  in  the  daytime.  Many  faint,  dark  lines  have  been 
noted  upon  it,  particularly  by  Lowell.  From  a  study  of  these  he 
infers  that  the  planet  rotates  on  its  axis  once  during  its  revolution 
around  the  sun.  The  fact  that  these  streaks  are  visible  shows  that 
the  planet  has  little  or  no  atmosphere.  When  it  passes  between  us 
and  the  sun  it  appears  like  a  sharp  disk  on  the  surface  of  the  sun, 
and  this  also  proves  the  absence  of  any  atmosphere.  This  result 
would  be  expected  because  the  small  gravitative  power  of  this  planet 
can  not  hold  an  atmosphere. 

Another  reason  for  believing  that  Mercury  has  no  atmosphere 
is  that  its  reflective  power  is  very  low.  The  observations  show  that 
it  reflects  only  about  17  per  cent  of  the  light  which  falls  upon  it,  which 


160  ASTRONOMY 

is  about  the  same  proportion  as  that  reflected  by  the  moon. 
Apparently  a  rough  surface  of  broken  rock  reflects  very  much  less 
light  than  an  atmosphere,  particularly  if  it  is  filled  with  clouds. 
Nearly  everyone  has  noticed  how  extremely  bright  clouds  of  the 
thunder-head  type  sometimes  are  in  the  sky.  These  clouds  appear 
very  luminous  because  we  see  the  light  side  of  them.  In  most  cases 
we  are  on  the  dark  side  of  clouds,  which  gives  us  the  impression 
that  they  are  dull  and  non-luminous.  The  fact  that  it  is  dark  below 
them  proves  that  they  either  reflect  or  absorb  a  large  part  of  the 
light,  and  that  consequently  if  we  were  on  the  upper  side  of  them 
they  would  appear  very  bright  to  us.  As  a  matter  of  fact,  the  clouds 
are  very  highly  reflective.  Anyone  who  has  seen  clouds  roll  around 
a  mountain  peak  knows  how  much  brighter  they  are  than  the  moun- 
tain unless  it  is  covered  with  snow. 

The  climatic  conditions  of  Mercury  are  most  extreme,  espe- 
cially if  one  side  is  always  toward  the  sun,  as  now  seems  to  be  the 
case.  This  side  is  exposed  perpetually  to  the  sun's  burning  rays 
at  a  distance  where  they  are  about  nine  times  as  intense  as  they 
are  on  the  earth.  The  other  side  is  never  favored  by  its  warmth  and 
light.  The  one  side  is  a  region  of  perpetual  torridity  and  the  other 
of  continual  frigidity.  There  is  a  zone  around  the  planet  at  which 
the  sun  is  near  the  horizon,  where  the  temperature  is  more  moderate. 
In  fact,  all  intermediate  states  between  the  hottest  and  the  coldest 
exist.  Almost  certainly  a  planet  in  the  state  in  which  Mercury  seems 
to  be  can  not  support  life  similar  to  that  which  flourishes  on  the 
earth. 

Venus,  as  distinguished  from  Mercury,  has  an  extensive  atmos- 
phere, as  is  indicated  by  its  great  brilliance,  reflecting  as  it  does 
76  per  cent  of  the  light  which  falls  upon  it,  and  by  the  illuminated 
ring  which  surrounds  it  when  it  passes  across  the  sun's  disk.  Fur- 
thermore, it  follows  from  the  kinetic  theory  of  gases  that,  since 
Venus  has  a  gravitative  power  at  the  surface  nearly  equal  to  that 
of  the  earth,  it  should  hold  an  atmosphere  as  the  earth  does. 

It  has  not  been  possible  to  detect  many  surface  markings  upon 
Venus  because  of  the  extensive  atmospheric  envelope  which  sur- 
rounds it.  At  the  present  time  it  is  impossible  to  say  even  what 
its  period  of  rotation  is.  Some  observers  have  supposed  they  found 
evidence  that  it  was  approximately  24  hours  and  other  observers 


ASTRONOMY  161 

have  been  equally  convinced  that  their  observations  have  shown 
them  that  it  always  keeps  the  same  face  toward  the  sun.  If  the 
former  conclusion  is  correct  the  succession  of  day  and  night  and  the 
seasonal  changes  on  Venus  are  very  similar  to  those  of  the  earth, 
though  because  of  its  nearness  to  the  sun  the  climate  should  be 
warmer.  If  the  latter  conclusion  is  correct  one  side  should  be  very 
warm — though  not  so  hot  as  the  corresponding  side  of  Mercury — 
and  the  other  side  very  cold.  The  reasons  for  the  difference  between 
Venus  and  Mercury  in  this  respect  are,  first,  that  Venus  is  farther 
from  the  sun  than  Mercury  is,  and  second,  that  the  temperature  of 
Venus  would  be  largely  equalized  by  the  atmosphere.  The  warm 
air  from  the  heated  side  would  continually  pass  to  the  colder  side, 
and  the  cooler  air  of  the  dark  side  back  to  the  heated  side.  There 
would  be  a  system  of  trade  winds  taking  the  heat  from  the  hot  to 
the  cool  side,  and  the  cool  air  back  to  the  heated  side. 

Mars.  The  planet  Mars  is  at  times  situated  more  favorably  for 
observations  from  the  earth  than  any  other  celestial  body  except  the 
moon.  Its  distance  from  the  earth  at  its  nearest  approach  is  about 
34,000,000  miles.  At  this  time  it  is  opposite  the  sun  in  the  sky  and 
appears  on  the  meridian  at  midnight  with  the  illuminated  side  toward 
the  earth. 

The  reflecting  power  of  Mars  is  low,  implying  in  accordance 
with  the-  discussion  made  above  that  it  has  a  small  atmosphere. 
Other  observations  confirm  this  conclusion.  Its  surface  is  nearly 
always  well  visible,  showing  rarely  any  indication  of  clouds.  Prob- 
ably the  only  clouds  that  are  observed  are  dust  storms. 

The  explanation  for  the  scanty  atmosphere  of  this  planet  is  that 
its  mass  is  so  small  and  its  surface  gravity  so  feeble  that  it  has  not 
power  to  control  one.  If  Mars  does  control  an  atmosphere,  probably 
it  is  made  up  largely  of  the  heavier  gases.  When  Mars  passes  between 
us  and  a  star  the  light  of  the  star  is  suddenly  extinguished  as  the 
edge  of  Mars  reaches  it.  If  Mars  had  an  extensive  atmosphere  the 
light  of  the  star  would  gradually  diminish  as  it  shone  through  more 
and  more  of  the  gaseous  envelope  surrounding  the  planet.  Probably 
atmospheric  pressure  on  Mars  does  not  exceed  that  on  the  top  of 
our  highest, mountains. 

The  planet  Mars  is  at  times  so  near  us  and  it  is  so  free  from 
an  obscuring  atmospheric  envelope  that  it  has  been  possible  for  a 


162  ASTRONOMY 

long  time  to  secure  accurate  observations  of  its  surface  markings. 
Fig.  77  shows  a  series  of  photographs  (made  by  Barnard  with  the 
great  40-inch  Yerkes  telescope)  of  one  side  of  Mars  on  which  can  be 
seen  large  shaded  areas  with  a  peninsular  projection  similar  to  that 
of  the  Indian  Peninsula  in  southern  Asia.  The  light-colored  part  of 


Fig.  77.     Mars  as  Photographed  with  the  Great  Yerkes  Telescope  by  Barnard 

Mars  is  actually  a  sort  of  dull  brick-colored  red,  and  it  is  this  which 
gives  it  its  ruddy  appearance  in  the  sky.  The  shaded  areas  have  a 
slightly  greenish  tinge.  From  observations  of  the  motions  of  these 
markings  across  the  disk  of  the  planet  it  has  been  possible  to  find 
its  period  of  rotation  with  a  very  high  degree  of  accuracy,  arid  also 
the  inclination  of  its  equator  to  the  plane  of  its  orbit.  The  day  of 


ASTRONOMY  163 

Mars  is  24  hours,  37  minutes,  22.7  seconds  long,  reckoned  in  our 
mean  solar  time.  The  inclination  of  the  plane  of  the  equator  of  Mars 
to  that  of  its  orbit  is  about  the  same  as  the  inclination  of  the  ecliptic. 
Therefore,  except  for  the  greater  distance  of  this  planet  from  the  sun, 
its  days  and  seasons  succeed  one  another  about  as  the  days  and 
seasons  of  the  earth  run  through  their  cycles. 

Besides  the  dark-shaded  areas  observed  on  the  planet,  there  are 
other  remarkable  details  which  have  been  seen  in  recent  years.  In 
1877  Schiaparelli,  an  Italian  observer,  working  with  a  modest  tele- 
scope of  8.75  inches  aperture,  but  favored  with  the  transparent 
Italian  skies,  found  that  Mars  was  crossed  and  recrossed  by  many 
dark-greenish  streaks  which  always  began  and  ended  in  the  dark 
areas  mentioned  above.  These  streaks  were  of  great  length  and 
invariably  extended  in  straight  lines,  that  is,  along  the  arcs  of  great 
circles.  They  varied  from  a  few  hundred  miles  in  length  up  to 
nearly  4,000.  These  streaks  were  called  by  Schiaparelli  canali 
(channels),  which  was  unfortunately  translated  into  "canals,"  a 
designation  altogether  too  suggestive,  for  there  is  no  guarantee  that 
they  have  any  analogy  with  canals  on  the  earth.  The  very  narrowest 
of  them  are  15  or  20  miles  across,  and  when  a  number  intersect  at  a 
point  there  is  generally,  if  not  always,  a  dark  knot  at  the  points  of 
intersection.  For  example,  seven  canals  converge  in  Lacus  Phoenicia 
and  six  in  Lacus  Lunae.  According  to  Lowell  the  junctions  of  canals 
are  always  provided  with  these  spots,  called  "lakes,"  and  conversely 
lakes  are  never  found  except  at  the  junctions  of  canals. 

In  the  winter  of  1881-82  Mars  was  again  in  favorable  position 
for  observation  and  Schiaparelli  studied  it  attentively  a  second  time. 
He  not  only  confirmed  his  preceding  observations,  but  he  found  that 
in  many  cases  there  were  two  canals  running  parallel  to  each  other 
for  long  distances.  This  doubling  was  found  to  depend  upon  the 
seasons  and  to  develop  with  astonishing  rapidity  especially  when  the 
sun  was  at  the  Martian  equinox. 

The  observations  of  Schiaparelli  have  been,  in  a  general  way, 
confirmed  by  Lowell  and  have  been  greatly  extended  by  him  during 
fifteen  years  of  observations  at  Flagstaff  and  in  Mexico  with  a  tele- 
scope of  24  inches  aperture.  He  has  found  in  addition  to  the  canals 
observed  by  Schiaparelli  many  others,  bringing  the  total  list  now  up 
to  over  400.  Lowell  describes  these  streaks  as  very  narrow  and 


164  ASTRONOMY 

thread-like,  and  of  remarkable  uniformity.  Fig.  78  shows  the  net- 
work of  canals  which  Lowell  discovered  on  Mars  from  many  obser- 
vations and  recorded  in  a  single  drawing. 

On  the  whole,  other  observers,  many  of  whom  have  had  wide 
experience  and  have  been  provided  with  large  instruments,  have  not 
been  able  to  confirm^  the  observations  of  Schiaparelli  and  Lowell. 


Fig.  78.      Mars  from  a  Drawing  by  Lowell 

This  negative  evidence  must  be  given  considerable  weight,  though,  of 
course,  positive  evidence  should  always  be  regarded  as  the  more  val- 
uable. There  have  been  many  astronomers  who  have  expressed  the 
opinion  that  in  some  way  the  observers  who  have  seen  the  line-like 
markings  on  Mars  have  been  deceived,  and  that  no  such  features  ex- 
ist there.  Experiments  have  shown  that  if  a  number  of  small  mark- 
ings be  placed  irregularly  on  a  disk,  and  the  disk  placed  at  such  a  dis- 


ASTRONOMY 


165 


tance  that  they  are  just  beyond  the  limit  of  distinct  visibility,  then  an 
observer  seeing  it  will  by  some  process  integrate  the  fine  markings 
into  lines.  Though  lines  do  not  exist  on  the  object  at  which  he  looks, 
he  will  apparently  see  them  under  these  circumstances.  Because  of 
this  fact,  the  suggestion  has  been  made  that  Mars  is  covered  with  a 
large  number  of  fine  spots  which  are  slightly  beyond  the  limits  of  dis- 


Fig.  79.     The  Disappearing  Polar  Caps  of  Mars  as  Observed  by  Barnard  at  the  Lick 
Observatory  in  1894 

tinct  vision  and  that  the  eyes,  particularly  of  some  observers,  integrate 
them  and  give  them  the  appearance  of  many  lines.  Of  course,  this 
conclusion  is  not  a  necessary  consequence  of  the  experiments. 

Besides  the  canals  on  Mars,  the  most  interesting  other  feature  is 
the  changing  polar  caps.  When  the  autumn  of  a  hemisphere  of  the 
planet  comes  on,  the  polar  region  extending  down  25  degrees  to  35 


166  ASTRONOMY 

degrees  from  the  pole  is  covered  with  a  white  mantle,  shining  with 
the  brilliance  of  snow.  This  white  covering  appears  suddenly,  remains 
all  winter,  and  disappears  gradually  in  the  spring,  sometimes  entirely 
vanishing  at  midsummer.  It  is  entirely  absent  during  the  summer 
and  reappears  again  rather  suddenly  in  the  autumn.  Fig.  79  shows 
a  series  of  drawings  of  the  diminishing  polar  cap  made  by  Professor 
Barnard  in  1894  at  the  Lick  Observatory.  The  slight  irregularities 
in  its  outline  prove  at  least  a  certain  degree  of  roughness  of  the 
surface  of  Mars.  While  these  polar  caps  have  every  appearance  of 
being  made  of  snow,  there  is  some  doubt  whether  this  is  the  true 
explanation  or  not.  In  the  first  place,  there  is  very  little  if  any 
water  upon  the  planet.  In  the  second  place,  it  is  not  perfectly  certain 
that  if  there  were  water  it  would  be  transferred  in  clouds  from  one 
region  to  another  and  precipitated  in  the  form  of  snow,  though  perhaps 
this  is  not  an  unreasonable  conclusion.  But  the  most  serious  question 
in  the  interpretation  of  these  polar  caps,  is  that  apparently  the  climate 
of  Mars  ought  to  be  considerably  colder  than  that  of  the  earth. 
Mars  is  so  much  farther  from  the  sun  than  the  earth  is,  that  it 
receives  less  than  half  as  much  light  and  heat  from  the  sun  as  the 
earth.  Using  this  fact  to  compute  the  theoretical  temperature  which 
it  would  have  if  its  atmospheric  conditions  were  the  same  as  those 
of  the  earth,  and  assuming  that  the  mean  temperature  of  the 
whole  earth  is  60°  F.,  it  turns  out  that  the  average  temperature  on 
Mars  should  be  38  degrees  below  zero.  With  such  a  temperature  as 
this  as  an  average  for  the  whole  planet,  taking  summer  and  winter 
together,  it  is  clear  we  should  not  expect  the  polar  cap  entirely  to 
disappear,  inasmuch  as  on  the  earth  it  is  a  permanent  feature.  Of 
course,  the  different  constitution  of  the  atmosphere  of  Mars  might 
account  for  a  considerable  difference,  but  it  certainly  would  seem  to 
strain  the  probabilities  to  suppose  that  a  very  rare  atmosphere  would 
have  such  a  constitution  that  it  could  make  a  variation  in  the  mean 
temperature  of  a  planet  of  60+ 38  =  98°  F.  And  even  this  is  not 
enough  to  account  for  the  entire  disappearance  of  the  polar  cap. 

One  suggestion  made  for  explaining  the  polar  cap  of  Mars  is 
that  it  is  carbon  dioxide  which  freezes  at  a  temperature  of  109°  F. 
If  the  atmosphere  of  Mars  contains  this  compound,  and  if  the  tem- 
perature falls  below  this  point,  it  would  freeze  and  be  deposited  on 
the  surface  as  a  white  substance  resembling  snow.  But  as  was 


ASTRONOMY  167 

mentioned  in  connection  with  the  discussion  of  the  earth's  atmosphere, 
carbon  dioxide  is  one  of  the  atmospheric  substances  which  tends  to 
produce  a  high  mean  temperature.  It  is  thus  apparent  that  this 
theory  is  at  least  to  some  extent  contradictory  to  itself .  At  the  present 
time  we  are  not  justified  in  drawing  any  positive  conclusion  about  the 
meaning  of  the  polar  cap  or  the  climatic  conditions  on  Mars. 

Assuming  that  the  polar  cap  is  snow  and  that  the  canals  on  Mars 
actually  exist  as  they  are  seen  by  a  few  observers,  the  question  of 
their  explanation  becomes  ore  of  considerable  interest.     W.  H.  Pick- 
ering suggested  the  idea  that  the  canals  are  streaks  of  vegetation. 
This  conclusion  is  to  some  extent  supported  by  the  fact  that  they 
appear  in  the  spring,  remain  visible  during  the  summer,  and  disappear 
in  the  autumn.  Lowell  pushes  the  theory  much  further  by  supposing 
that  the  canals  are  streaks  of  vegetation  which  grow  because  the 
territory  where  they  appear  is  irrigated.    This  implies  the  existence 
of  life  and  a  high  order  of  intelligence  on  Mars.     He  supposes  that 
these  intelligent  creatures  have  dug  waterways  from  the  dark  regions, 
which  he  interprets  as  being  marshy  regions,  for  hundreds   and  in 
some  cases  thousands  of  miles,  out  across  the  brick-red  parts,  which 
he  interprets  as  being  burning  deserts.    Leading  out  from  the  sides  of 
these  irrigation  ditches  he  supposes  there  are  lateral  canals  which 
reach  to  a  distance  of  10  to  25  miles.    In  this  manner  he  supposes 
a  streak  from  15  to  50  miles  wide  and  from  a  few  hundred  to  three 
or  four  thousand  miles  long  is  irrigated.    In  the  winter  time  vegetation 
would  be  dead,  certainly  if  it  were  analogous  to  that  on  the  earth, 
and  the  streaks  would  be  invisible.     As  the  spring  approaches,  the 
polar  caps  would  melt  and  the  marshy  regions  would  fill  up,  the 
water  would  be  led  out  through  the  main  irrigation  ditches  and  intty 
the  laterals,  thus  supplying  the  ground  with  the  moisture  necessary 
for  the   development   of  vegetation.     Having  then  the  increasing 
warmth  and  the  needed  supply  of  water,  he  supposes  vegetation 
would  spring  up  and  flourish.    This  would  give  the  areas  on  which  it 
grew  a  dark  color,  as  contrasted  with  the  red  of  the  soil.    The  places 
where  the  canals  cross  would  be  irrigated  regions  of  unusual  size  and 
probably  would  be  the  seats  of  considerable  population. 

Lowell's  theory  is  interesting,  even  if  it  is  somewhat  fantastic. 
There  are  serious  difficulties  in  the  way  of  accepting  it,  aside  from 
the  question  of  the  climatic •  conditions  on  the  planet.  One  of  these 


168  ASTRONOMY 

is  that  it  is  not  a  sign  of  intelligence  to  construct  canals  thousands  of 
miles  long,  in  straight  lines,  and  of  uniform  width,  irrespective  of  the 
irregularities  of  the  surface  of  the  planet  and  the  variations  in  the 
fertility  of  its  soil.  The  irregularities  of  the  borders  of  the  polar  cap 
prove  that  the  surface  is  far  from  being  smooth,  and  in  fact  the 
division  of  it  into  red  regions  and  dark  regions  shows  that  it  is  by 
no  means  uniform.  It  is  reasonable  to  suppose,  in  view  of  what  we 
know  of  the  earth  and  the  moon,  that  all  of  it  is  more  or  less 
irregular.  If  it  has  had  an  origin  similar  to  that  of  the  earth,  and  if 
it  has  had  an  evolution  similar  to  that  of  the  earth,  then  the  character 
of  its  soil  should  vary  from  place  to  place,  like  that  of  the  earth. 
Certainly  these  are  the  probabilities.  It  seems  most  remarkable, 
then,  that  these  creatures  who  are  assumed  to  be  intelligent  should 
make  their  canals  of  absolutely  uniform  width  and  in  absolutely 
straight  lines.  Besides,  it  is  not  evident  why  it  is  economical  to  run 
canals  3,500  miles  from  the  source  of  water,  when  there  is  abundant 
unirrigated  territory  in  the  immediate  vicinity.  The  expense  of  this 
is  certainly  enormous.  If  vegetation  requires  the  same  amount  of 
water  there  that  it  does  on  the  earth  in  order  to  flourish,  the  canal 
system  and  Lowell's  interpretation  of  it  imply  that,  for  every  ton  of 
vegetable  matter  that  is  raised  on  Mars,  on  the  average  one  thousand 
tons  of  water  are  transported  along  the  canals  one  thousand  miles. 
It  is  only  fair  to  the  reader  to  state  that  while  Lowell  has  urged  his 
views  very  strongly,  astronomers  are  almost  universally  extremely 
skeptical  regarding;  them. 

Granting  that  Lowell's  theory  is  correct,  one  is  still  likely  to 
draw  quite  erroneous  conclusions.  If  there  is  life  on  Mars  and  a 
high  order  of  intelligence,  there  is  no  reason  to  suppose  that  the 
beings  of  highest  intellectual  development  are  physically  anything 
like  men.  The  animals  on  the  earth,  and  human  beings  among  them, 
are  adapted  to  their  surroundings,  for  if  they  were  not  more  or  less 
perfectly  adjusted  to  them  they  would  perish.  For  example,  our 
skeletons  are  made  of  bones  strong  enough  to  support  us  and  permit 
of  certain  activities  when  we  are  subject  to  certain  gravitative  forces; 
our  lungs  are  adjusted  to  the  atmosphere  in  which  we  live;  and  the 
amount  of  water  on  the  earth  and  in  its  atmosphere  is  an  important 
factor  in  the  life  processes,  and  animals  on  the  earth  are  adjusted 
to  these  conditions.  On  the  planet  Mars  nearly  all  of  the  fundamental 


ASTRONOMY 


conditions  are  radically  different  from  those  on  the  earth.  For 
example,  the  surface  gravity  is  much  less,  the  atmospheric  pressure 
is  only  a  small  fraction  of  what  it  is  here,  the  constitution  of  the 
atmosphere  may  be  quite  different,  the  intensity  of  solar  radiation 
is  less  than  half  that  on  the  earth,  and  the  amount  of  water  is  a  very 
small  fraction  of  that  on  the  earth.  Consequently,  if  life  does  flour- 
ish on  Mars,  then  it  must  physically  be  very  different  from  that  on 
the  earth.  Of  course,  there  is  no  fundamental  reason  why  it  should 
not  be  different. 

Granting  that  there  is  life  on  Mars  and  that  in  its  physical 
aspects  it  is  suited  to  its  environment,  we  are  still  likely  to  draw 
erroneous  conclusions  regarding  the  organization  of  what  we  may 
call  its  society.  There  is  no  reason  for  assuming  that  there  are  social 
and  political  conditions  on  another  planet  anything  like  those  which 
are  on  the  earth.  If  there  is  life  there,  thousands  or  millions  of  years 
ago  it  may  have  passed  through  that  stage  of  evolution  correspond- 
ing to  the  one  in  which  we  now  struggle.  When  one  thinks  of  the 
remarkable  changes  which  society  has  undergone  in  a  few  centuries, 
the  significance  of  such  a  statement  becomes  clear.  At  the  rate 
human  relations  have  been  changing,  in  a  few  thousand  years  from 
now  social  conditions  will  be  ab- 
solutely unlike  those  existing  at 
present.  Hence,  it  is  clear  that 
even  though  the  physical  condi- 
tions on  another  world  were  like 
those  here,  there  would  be  no 
reason  for  assuming  a  general 
similarity  in  the  mode  of  life  and 
state  of  society. 

The  planets  Mercury  and 
Venus  have  no  satellites,  so  far 
as  known,  but  Mars  is  attended 
by  two  very  small  moons  re- 
volving from  west  to  east 

around  it  sensibly  in  the  plane  of  its  equator.  They  are  so 
small  and  so  near  the  bright  planet  that  they  were  not  dis- 
covered until  1877,  when  Hall  found  them  with  the  great  telescope 
of  the  Naval  Observatory  at  Washington.  They  can  be  seen 


Fig.  80.     The  Orbits  of  the  Satellites  of 
Mars  and  the  Planet  on  the  Same  Scale 


170  ASTRONOMY 

only  with  a  few  of  the  largest  telescopes  in  the  world.  Hall  named 
these  satellites  Phobus  and  Deimos.  Phobus  is  5,850  miles  from 
the  center  of  the  planet,  or  only  3,750  miles  from  its  surface.  Deimos 
is  distant  14,650  miles  from  the  center  of  the  planet.  Fig.  80  gives 
the  planet  and  the  orbits  of  its  two  satellites  to  scale. 

The  diameters  of  the  satellites  of  Mars  are  probably  approxi- 
mately ten  miles.  They  are  so  small  that  they  can  not  be  measured 
directly,  and  can  only  be  inferred  from  the  amount  of  light  they 
send  us.  On  a  body  so  small  as  these  satellites  and  having  the 
density  of  the  earth,  an  object  which  would  weigh  one  pound  on  the 
earth  would  weigh  only  7V  of  an  ounce. 

One  consequence  of  the  nearness  of  the  satellites  to  the  planet 
is  their  rapid  revolution  around  it.  The  period  of  revolution  of 
Phobus  is  7  hours  and  39  minutes,  and  that  of  Deimos  30  hours 
and  18  minutes.  It  follows  from  this  that  Phobus  goes  around  the 
planet  in  about  one-third  of  its  period  of  rotation.  Phobus  and  the 
planet  both  go  to  the  east,  but  Phobus  the  faster.  Therefore,  the  re- 
markable situation  is  realized  of  a  satellite  rising  in  the  west  and 
setting  in  the  east.  The  period  of  Phobus  from  meridian  around  to 
meridian  again  is  11  hours  and  7  minutes,  or  a  little  less  than 
half  a  day.  This  satellite  then  runs  through  all  the  changes  of  its 
phases  between  sundown  and  sunrise.  On  the  other  hand,  Deimos, 
whose  period  is  longer  than  that  of  the  rotation  of  Mars,  rises  in  the 
east  and  sets  in  the  west,  the  mean  period  from  meridian  to  meridian 
being  131  hours  15  minutes. 

Jupiter.  Jupiter  is  a  very  bright  object  in  the  sky,  its  mag- 
nitude depending  upon  its  great  ^size  and  the  high  reflective  power 
of  its  surface.  When  the  computations  are  made  it  is  found  that 
Jupiter  reflects  about  two-thirds  of  the  sunlight  which  falls  upon  it. 
From  this  it  can  be  inferred  that  it  has  an  extensive  atmosphere. 
This  conclusion  is  supported  by  many  other  considerations.  The 
mean  density  of  the  planet  is  very  low  and  probably  we  never  have 
seen  its  solid  surface  if,  indeed,  it  has  any. 

As  seen  through  a  telescope  Jupiter  is  characterized  by  a  series 
of  bright  bands,  alternately  light  and  dull  brown,  running  parallel 
to  its  equator.  These  bands  vary  in  width  and  number,  but  are 
generally  from  1,000  to  10,000  miles  wide.  They  are  most  con- 
spicuous near  the  equator,  and  the  equator  is  generally  covered  by  a 


ASTRONOMY  171 

light  band.  At  the  present  time  it  is  8,000  or  10,000  miles  wide. 
In  1882,  according  to  the  drawing  of  Hough,  who  for  many  years  fol- 
lowed this  planet  carefully,  the  equator  was  entirely  covered  by  a 
union  of  the  dark  bands  which  are  on  each  side  of  it.  Fig.  81  shows 
Jupiter  as  it  has  appeared  in  recent  years. 

One  of  the  most  conspicuous  features  ever  seen  upon  Jupiter 
is  what  is  known  as  the  great  red  spot,  which  was  until  recently  a 
pale  pinkish  oval  extending  parallel  to  the  equator  for  30,000  miles 
and  in  the  opposite  direction  7,000  miles.  It  appeared  rather  sud- 
denly in  1878  beneath  the  southern  red  belt.  In  a  year  after  its 
appearance  it  had  changed  to  a  bright  red  color,  and  was  the  most 


Fig.  81.     The  Planet  Jupiter  as  Drawn  by  Barnard 

conspicuous  object  visible  on  the  planet.  Since  that  time  it  has 
undergone  many  changes  both  of  color  and  brightness,  and  though 
much  diminished  in  intensity  is  yet  generally  faintly  visible. 

From  observations  of  the  spots  and  other  distinct  markings 
on  Jupiter  the  period  of  its  rotation  on  its  axis  has  been  found  to 
be  on  the  average  about  9  hours  and  54  minutes.  No  other  celestial 
body  is  known  whose  period  of  rotation  is  so  short  as  this.  It  is 
necessary  to  speak  of  the  rotation  on  the  average  because  there  are 
great  variations  among  the  spots,  particularly  when  they  are  in 


172  ASTRONOMY 

different  latitudes.  Some  markings  have  been  observed  which  give 
a  period  of  9  hours  50  minutes,  while  others  give  a  period  so  long 
as  9  hours  and  57  minutes,  or  an  extreme  difference  of  about  ^\  of 
the  whole  period.  And  since  the  circumference  of  the  whole  planet 
is  nearly  300,000  miles,  it  follows  that  the  rate  of  rotation  at  the 
equator  is  about  30,000  miles  an  hour.  Therefore,  two  spots  whose 
difference  in  motion  is  -gV  the  motion  of  either  have  a  drift  relative 
to  each  other  of  about  350  miles  per  hour.  On  the  earth  the  most 
violent  tornadoes  we  ever  have  are  produced  by  wind  velocities 
not  much  exceeding  100  miles  an  hour.  The  variation  in  the  rate  of 
rotation  of  the  different  parts  of  Jupiter  is  not  entirely  irregular. 
As  a  rule  the  equatorial  parts  rotate  most  rapidly.  There  are, 
however,  some  dissimilarities  between  the  two  hemispheres.  On 
the  whole  the  southern  hemisphere  presents  evidence  of  more  rap'd 
changes  in  the  spots,  and  perhaps  greater  relative  motions  among 
them.  More  remarkable  than  these  variations  in  motion  from  spot 
to  spot,  is  the  fact  that  sometimes  the  rate  of  motion  of  a  single  spot 
changes  considerably.  For  example,  the  period  of  rotation  of  the 
great  red  spot  increased  seven  seconds  in  the  first  eight  years  follow- 
ing its  discovery,  but  since  that  time  it  has  remained  sensibly  con- 
stant. There  is  no  conclusive  explanation  of  the  reason  why  the 
various  zones  of  Jupiter  rotate  with  different  periods,  or  why  the 
rates  of  rotation  of  the  different  spots  vary  from  time  to  time. 

It  follows  from  the  low  density  of  Jupiter  and  the  relatively 
rapid  changes  on  its  surface  that  there  are  probably  no  fixed  features 
on  it  whatever.  Probably  this  planet  is  largely  gaseous,  though  the 
pressure  at  great  depths  is  so  great  that  it  may  be  the  laws  of  gases 
are  not  strictly  obeyed.  The  surface  gravity  is  2.6  times  that  of  the 
earth,  and  this  indicates  that  there  are  enormous  pressures  in  the 
depths  of  the  planets.  The  fact  that  Jupiter  has  a  low  density  in 
spite  of  high  pressures,  leads  to  the  conclusion  that  either  this  planet 
is  made  up  largely  of  very  rare  materials,  or  that  it  has  a  very  high 
temperature.  It  has  often  been  supposed  that  its  surface  is  itself 
hot  and  partly  self-luminous.  One  can  scarcely  escape  this  conclu- 
sion when  he  looks  into  the  sky  at  Jupiter  and  sees  how  exceedingly 
brilliant  it  is.  It  stretches  his  imagination  to  believe  that  the  light 
which  he  sees  is  all  sunlight  which  has  been  reflected  from  the  sur- 
face of  the  planet.  Nevertheless,  it  is  certain  that  Jupiter  radiates 


ASTRONOMY  173 

directly  no  sensible  quantity  of  light.  As  we  shall  see,  this  planet  has 
many  satellites  and  when  they  pass  between  it  and  the  sun  their 
shadows  fall  upon  it.  If  Jupiter  were  self-luminous  the  places  where 
the  shadows  strike  would  still  be  bright,  the  brightness  depending 
upon  its  luminosity.  But  the  actual  observations  show  that  where 
the  shadows  fall  Jupiter  is  very  black  indeed.  If  the  satellites  should 
pass  into  the  shadow  of  Jupiter,  they  would  be  st'll  somewhat  il- 
luminated if  Jupiter  itself  were  luminous,  but  we  find  that  if  they 
pass  behind  Jupiter  so  that  all  the  sunlight  is  cut  off  from  them,  they 
instantly  become  totally  invisible.  From  this  we  conclude  that, 
although  the  planet  may  be  very  hot  throughout  most  of  its  volume, 
its  surface  is  yet  so  cool  that  it  gives  out  no  sensible  quantity  of  light. 

The  inclination  of  the  plane  of  Jupiter's  equator  to  that  of  its 
orbit  is  only  three  degrees.  The  eccentricity  of  its  orbit  is  very  small. 
Consequently  there  are  no  marked  seasonal  changes  on  this  planet. 
Jupiter  is  a  little  more  than  five  times  as  far  from  the  sun  as  the  earth 
is,  and  therefore  gets  less  than  ^Y  as  much  light  and  heat.  If  it  were 
situated  similarly  to  the  earth  and  had  an  atmosphere  similar  to  that 
which  surrounds  the  earth,  its  mean  temperature  would  be  extremely 
low.  If  planets  go  through  an  evolution  from  those  primitive  condi- 
tions in  which  we  find  Jupiter  at  the  present  time  to  those  the  earth  is 
in  now,  and  perhaps  on  to  dead  worlds  like  the  moon,  certainly  Jupiter 
when  it  loses  its  heat  will  lapse  into  a  condition  of  perpetual  frigidity. 

Jupiter  is  surrounded  by  a  remarkable  family  of  satellites. 
Four  of  them  are  large,  ranging  in  diameter  from  2,000  to  3,600 
miles.  They  were  the  first  celestial  objects  ever  discovered  with 
a  telescope,  and  were  first  seen  by  Galileo  in  1610.  They  are  barely 
beyond  the  limits  of  visibility  without  optical  aid  and,  indeed,  could 
be  seen  with  the  unaided  eye  if  they  were  not  lost  in  the  dazzling  rays 
of  the  planet.  No  other  satellite  of  Jupiter,  besides  these  four,  was 
discovered  until  1892  when  Barnard,  then  at  the  Lick  Observatory, 
caught  a  glimpse  of  a  fifth  one  very  close  to  the  planet.  It  is  so  small 
and  so  buried  in  the  rays  of  the  great  planet  that  it  can  be  seen  only 
by  experienced  observers  through  a  few  of  the  largest  telescopes  in 
the  world.  Since  1905  three  new  satellites  revolving  at  great  dis- 
tances from  the  planet  have  been  discovered.  Two  are  at  a  distance 
of  about  6,500,000  miles  from  the  center  of  the  planet,  and  the  third 
is  distant  about  12,000,000  miles. 


174 


ASTRONOMY 


The  distances  of  the  satellites  range  from  100,000  miles  to 
12,000,000  miles;  the  periods  from  about  12  hours  to  550  days.  The 
periods  are  much  shorter  than  they  would  be  for  a  planet  of  a  smaller 
mass.  For  example,  the  satellite  nearest  Jupiter  of  the  four  which 
Galileo  discovered,  which  is  numbered  1  and  named  lo,  revolves  at 
a  distance  of  261,000  miles.  This  is  a  little  greater  than  the  distance 

of  the  moon  from  the  earth, 
but  in  spite  of  this  fact  its 
period  instead  of  being  27 
days  is  less  than  2  days. 
This  is,  of  course,  due  to  the 
greater  attractive  power  of 
the  planet  Jupiter,  and,  as 
was  explained  above,  gives 
us  a  means  of  determining  the 
mass  of  Jupiter.  Fig.  82  gives 
Jupiter  and  the  orbits  of  the 
five  inner  satellites  to  scale. 

A  very  remarkable  dis- 
covery was  made  in  connec- 
tion with  Jupiter's  satellites, 
in  1675,  by  the  Danish  astronomer  Romer.  The  period  of  revo- 
lution of  Jupiter's  satellites  can  be  determined  from  the  times 
when  they  pass  into  the  shadow  of  the  planet  and  become  invisible. 


Fig.  82.     Jupiter  and  the  Orbits  of  Five  of  Its 
Satellites  on  the  Same  Scale 


Fig.  83.    The  Discovery  of  the  Velocity  of  Light  from  Eclipses  of  Jupiter's  Satellites 

Their  periods  were  determined  when  the  earth  was  on  the  side  of 
its  orbit  towards  the  planet,  as  at  El  in  Fig.  83.  Having  deter- 
mined the  period,  it  was  possible  to  predict  the  times  when  the 


ASTRONOMY  175 

eclipses  should  occur.  A  few  months  later  when  the  earth  got  to  the 
position  E2,  and  Jupiter  to  J2,  it  was  found  that  the  eclipses  did  not 
occur  at  the  predicted  times,  but  a  few  minutes  later.  It  was  inferred 
from  this  that  the  reason  they  were  delayed  was  not  that  the  satellites 
moved  around  Jupiter  with  different  periods,  but  that  the  light  had 
farther  to  come  to  the  earth.  After  the  satellite  passes  into  the 
shadow  of  Jupiter,  it  is  still  visible  to  the  earth  until  the  last  light 
which  leaves  it  before  it  passes  into  the  shadow,  reaches  the  earth. 
The  distance  from  J2  to  E2  is  nearly  180,000,000  miles  greater  than 
the  distance  from  Jl  to  Et.  Consequently,  if  light  does  not  travel 
with  infinite  speed,  the  eclipses  should  be  as  many  minutes  late  when 
observed  from  E2  as  it  takes  light  to  travel  over  the  difference  of 
these  distances.  It  was  found  from  the  calculations  that  the  obser- 
vations could  be  explained  under  the  theory  that  light  travels  at 
the  rate  of  about  200,000  miles  per  second. 

The  finite  velocity  of  light  has  been  proved  in  many  other 
ways.  It  has  not  been  necessary  to  appeal  to  celestial  phenomena 
in  order  to  determine  its  rate,  but  it  has  been  measured  on  the  sur- 
face of  the  earth  by  a  number  of  experimenters.  The  work  of  Fizeau, 
Michelson,  and  Newcomb  shows  that  the  velocity  of  light  is  very 
nearly  186,330  miles  per  second.  It  follows  from  this  that  it  takes 
light  about  499  seconds,  or  a  little  more  than  8  minutes,  to  come 
from  the  sun  to  us.  Therefore,  when  anything  takes  place  upon  the 
sun  it  is  not  seen  here  until  8  minutes  later.  The  distance  of 
Jupiter  is  so  great  that  it  takes  about  an  hour  and  a  quarter  for  light 
to  go  to  it  from  the  sun  and  back  to  the  earth. 

Saturn.  In  many  respects  Saturn  is  the  most  interesting 
planet  in  the  solar  system.  It  is  distinguished  by  a  remarkable 
system  of  rings  which  surround  it  in  the  plane  of  its  equator.  Fig. 
84  shows  the  general  appearance  of  the  rings  according  to  a  drawing 
made  by  Barnard.  The  extreme  diameter  of  the  outer  ring  is  approxi- 
mately 175,000  miles.  Between  the  outer  ring  and  the  brightest  one 
is  a  vacant  space  about  2,200  miles  in  width.  This  is  known  as 
Cassini's  division,  having  been  discovered  by  the  French  astronomer 
Cassini.  Inside  of  Cassini's  division  is  the  brightest  ring,  whose 
width  is  about  18,000  miles.  Near  its  exterior  it  is  brilliantly  luminous, 
shining  as  brightly  as  the  planet  itself,  but  it  fades  out  gradually 
toward  its  interior  border.  Inside  of  the  bright  ring  is  a  fainter  ring 


176 


ASTRONOMY 


known  as  the  crepe  ring,  which  was  discovered  simultaneously  in  this 
country  and  in  England  about  fifty  years  ago.  Its  width  is  about 
11,000  miles.  Then  between  the  inner  edge  of  the  crepe  ring  and  the 
planet  is  a  gap  of  about  6,000  miles. 

The  ring  is  very  thin,  as  is  shown  by  Barnard's  drawing,  Fig. 
85,  when  it  was  almost  edgewise  to  the  earth  in  1907.  When  it 
was  exactly  edgewise  it  became  invisible  even  through  the  great 
Yerkes  telescope.  It  follows  from  this  that  its  thickness  can  not 
exceed  50  miles.  If  one  should  draw  a  map  of  Saturn  and  the  ring 
system,  making  the  whole  diameter  of  the  ring  system  five  inches, 
on  the  same  scale  the  thickness  would  be  onl  T  of  an  inch. 


Fig.  84.     Saturn  and  Its  Rings  from  a  Drawing  Made  by  Barnard 

The  bright  rings  appear  to  be  as  solid  and  as  continuous  as  the 
planet  itself.  For  many  years  after  their  discovery  by  Galileo,  it 
was  supposed  that  they  were  perhaps  composed  of  solid  or  liquid 
material.  It  was  proved  by  Laplace  that  such  a  constitution  is 
impossible.  If  they  were  solid  the  attraction  of  the  planet  would  crush 
them  unless  they  were  made  of  stronger  material  than  anything  we 
know.  It  is  easy  to  see  that  a  solid  ring  is  dynamically  similar  to 
an  arched  bridge,  the  difference  being  that  the  ends  of  it  do  not  rest 
upon  the  planet  but  upon  other  portions  of  the  ring.  If  the  ring  is 
supposed  to  rotate  around  the  planet  the  difficulties  are  relieved  to 
some  slight  extent.  If  it  is  supposed  to  rotate  fast  enough  so  that 


ASTRONOMY  177 

the  centrifugal  acceleration  of  the  interior  part  balances  the  attrac- 
tion of  the  planet  for  it,  then  the  centrifugal  acceleration  of  the  outer 
part  will  be  much  too  great  and  there  will  be  a  tendency  for  it  to  fly 
into  fragments.  Even  if  it  were  made  of  material  a  hundred  times 
stronger  than  any  material  with  which  we  are  familiar  on  the  earth, 
still  it  could  not  remain  permanent  in  that  form  if  it  were  in  the  solid 
state.  A  liquid  state  is  equally  impossible.  Consequently  there  re- 
mains only  one  hypothesis,  and  that  is  that  it  is  made  up  of  a  vast 
swarm  of  small  particles  circulating  around  the  planet  in  the  plane 
of  the  planet's  equator.  This  theory  was  suggested  nearly  two  hun- 
dred years  ago  but  was  not  generally  adopted  until  recent  times. 
Under  this  hypothesis  every  separate  particle  moves  like  a  satellite 


Fig.  85.     The  Rings  of  Saturn  When  They  are  Nearly  Edgewise  Toward  the 
Earth — After  a  Drawing  by  Barnard 

free  from  all  the  others  except  at  times  of  possible  collision.  Accord- 
ing to  this  theory  those  particles  which  are  nearest  the  planet  move 
most  rapidly,  and  those  which  are  farthest  move  most  slowly,  and 
the  difference  is  a  precise  amount  depending  upon  the  attraction  of 
the  planet  and  the  difference  in  distance.  It  is  possible  to  compute 
theoretically  what  this  difference  should  be.  About  20  years  ago 
the  spectroscope  was  used  to  determine  how  these  particles  moved, 
and  it  was  found  that  their  motions  were  in  perfect  harmony  with  the 
theory  that  the  rings  are  made  up  of  a  great  swarm  of  small  particles 
which  revolve  independently  of  one  another. 

It  might  be  supposed  that  there  are  difficulties  in  accounting 
for  the  appearance  of  solidity  of  the  rings  of  Saturn  on  the  dust- 


178  ASTRONOMY 

cloud  theory.  One  might  imagine  that  they  should  be  more  nearly 
transparent  than  they  are.  But  the  incorrectness  of  this  view  is  at 
once  evident  when  we  consider  how  opaque  are  the  clouds  in  our 
own  atmosphere.  Clouds  are  made  up  of  small  drops  of  water  in 
great  numbers  and  form  opaque  screens,  though  often  they  are  not 
more  than  half  a  mile  thick.  Consequently,  it  is  easy  to  see  how 
a  swarm  of  dust  particles,  possibly  as  much  as  fifty  miles  in  thick- 
ness, might  have  the  appearance  of  being  perfectly  solid.  With 
such  a  thickness  it  is  not  necessary  to  suppose  the  particles  are  very 
close  to  one  another  or  that  collisions  very  frequently  take  place. 

The  planet  itself  is  somewhat  similar  to  Jupiter,  though  the 
markings  on  it  are  less  distinct.  There  is  a  bright  equatorial  belt 
and  many  slightly  darker  zones  in  the  higher  altitudes.  The  polar 
regions  are  generally  darker  than  any  other  part  of  the  planet.  It 
has  been  difficult  to  find  spots  which  are  lasting  enough  and  con- 
spicuous enough  to  enable  the  observers  to  determine  the  period  of 
Saturn's  rotation.  But  those  determinations  which  have  been  made 
show  that  this  planet  rotates  on  its  axis  in  a  little  more  than  10  hours. 
It  is  also  similar  to  Jupiter  in  the  fact  that  its  equatorial  zone  rotates 
more  rapidly  than  its  higher  latitudes.  Likewise  there  are  relative 
drifts  of  different  parts  at  high  speed.  Some  portions  have  been 
observed  to  pass  by  others  at  the  rate  of  600  or  700  miles  per  hour. 

Since  Saturn  has  a  density  considerably  less  than  water  one 
would  not  expect  to  find  in  it  any  solid  material,  at  least  near  its 
surface.  The  changing  and  unstable  character  of  the  markings 
which  are  observed  harmonizes  perfectly  with  this  conclusion.  It 
is  almost  certain  that  Saturn  is  gaseous  to  a  great  depth,  and  per- 
haps throughout.  The  planet  is  certainly  in  an  early  stage  of  its 
evolution  and  will  not  become  suitable  for  the  existence  and  develop- 
ment of  life  until  after  it  undergoes  enormous  changes. 

The  plane  of  Saturn's  equator  is  inclined  to  that  of  its  orbit  by 
27  degrees.  For  this  reason  the  seasonal  changes  would  be  marked. 
But  Saturn  is  so  far  from  the  sun  that  it  receives  only  ^  as  much 
light  and  heat  per  unit  area  from  the  sun  as  the  earth  does.  It  fol- 
lows that  if  its  atmospheric  constitution  were  anything  like  that  of 
the  earth  it  would  be  continually  frozen,  even  in  its  equatorial 
regions,  and  consequently  that  the  seasonal  changes  would  not  be 
important.  But  here,  as  in  the  consideration  of  all  the  planets,  the 


ASTRONOMY 


179 


constitution  of  the  atmosphere  is  an  important  factor  which  must 
not  be  neglected. 

Saturn  has  more  known  satellites  than  any  other  planet.  The 
last  two  of  the  ten  were  discovered  by  photography.  The  one  nearest 
to  Saturn  is  distant  from  its  center  117,000  miles;  the  one  farthest 
is  distant  about  8,000,000  miles.  Their  periods  of  revolution  vary 
from  about  225  hours  to  550  days.  The  periods  are  shorter  than 
they  would  be  for  satellites  revolving  around  the  earth  at  the  same 


Fig.  86.     Saturn's  Satellite  System,  with  the  Exception  of  the 
Ninth,  on  the  Same  Scale 

distances,  but  somewhat  longer  than  they  would  be  for  planets 
revolving  around  Jupiter  at  the  same  distances.  These  satellites 
vary  in  diameter  from  100  or  200  miles  to  3,000  miles.  Fig.  86  is  a 
map  of  Saturn's  satellite  system  (with  the  exception  of  the  ninth 
which  is  so  far  away  it  can  not  be  shown)  in  which  the  dot, at  the 
center  represents  the  planet.  A  remarkable  thing  about  these 
satellites  is  that  all  of  them  revolve  from  west  to  east  with  the  excep- 
tion of  the  ninth  which  revolves  in  the  opposite  direction. 

Uranus.  Uranus  is  so  far  from  the  sun  that  it  appears  in  the 
sky  as  a  faint  object  of  the  sixth  magnitude.  It  was  discovered  in 
1781  by  Sir  William  Herschel,  who  was  then  carrying  out  his  pro- 


180  ASTRONOMY 

gram  of  sweeping  the  whole  sky  for  interesting  objects.  Herschel 
as  a  young  man  was  a  professional  musician  and  originally  took  up 
astronomy  only  as  a  pastime.  His  imagination  became  fired  by  the 
mysteries  of  the  heavens  and  he  determined  to  explore  them  so  far 
as  was  in  his  power.  In  those  days  it  was  not  possible  to  buy  a  tele- 
scope for  a  relatively  small  amount  of  money,  as  it  is  now.  Con- 
sequently, if  he  were  to  have  an  instrument  he  must  make  it  himself. 
Accordingly,  he  took  up  the  study  of  the  theory  of  optical  instru- 
ments and  of  other  branches  of  mathematics  and  astronomy.  With 
his  own  hands  he  made  many  telescopes.  It  was  with  one  of  these 
that  he  discovered  the  planet  Uranus.  One  night  in  his  sweeping 
of  the  sky  he  detected  an  object  which,  though  nearly  like  a  star, 
differed  from  a  star  in  having  a  very  small  disk.  Through  a  tele- 
scope, no  matter  how  powerful  it  may  be,  the  stars  still  appear  as 
points  of  light,  though,  of  course,  much  brighter  than  without  an 
instrument.  But  the  planets  have  sensible  disks,  their  apparent  size 
depending  upon  their  actual  size  and  their  distance  from  the  observer. 
Now,  Uranus  is  so  far  away  that  its  disk  is  apparently  very  small 
even  when  seen  through  a  large  telescope.  It  is  remarkable  that 
Herschel  should  have  noticed  that  it  differed  in  appearance  from  a 
star.  At  first  he  did  not  suspect  that  he  had  found  a  new  planet.  He 
informed  his  friends  of  the  peculiar  object  which  he  had  seen  and 
expressed  his  opinion  that  it  might  be  a  comet.  If  it  were  not  a 
star  its  position  would  change  rapidly  with  respect  to  them.  Obser- 
vations showed  in  a  few  days  that  it  was  moving  and  in  a  few 
weeks  that  instead  of  being  a  comet  it  was,  indeed,  a  new  planet. 
This  was  the  first  world  discovered  in  historic  times.  It  immediately 
attracted  the  widest  interest.  George  III.,  who  was  then  king  of 
England,  appointed  Herschel  royal  astronomer  and  he  thenceforth 
devoted  all  his  life  to  the  study  of  astronomy. 

Four  satellites  have  been  discovered  revolving  about  Uranus. 
They  all  move  sensibly  in  the  same  plane,  which  is  almost  at  right 
angles  to  the  plane  of  the  planet's  orbit.  If  the  planet's  equator 
is  in  the  plane  of  the  orbits  of  the  satellites,  as  we  may  perhaps  infer 
from  analogy  with  the  other  planets,  particularly  Jupiter  and  Saturn, 
then  the  inclination  of  its  equator  to  the  plane  of  its  orbit  is  about 
90  degrees.  A  planet  with  such  a  relation  of  its  axis  of  rotation  to  its 
plane  of  revolution  would  not  have  seasons  in  .any  respect  similar 


ASTRONOMY  181 

to  our  own.  However,  this  is  not  an  important  question  in  the  case  of 
a  planet  so  far  from  the  sun  as  Uranus  is,  because  if  the  surface  con- 
ditions and  atmosphere  are  at  all  similar  to  those  of  the  earth,  its  mean 
temperature  must  be  many  degrees  below  zero  even  at  the  equator. 

Uranus  is  so  far  from  the  sun  and  the  earth,  being  at  its  nearest 
to  the  earth  about  1,600,000,000  miles  away,  that  no  surface  markings 
have  been  detected  on  it  by  means  of  which  its  rotation  can  be  deter- 
mined. The  only  hope  at  present  of  finding  its  rate  of  rotation  is 
from  the  effects  of  an  equatorial  bulge,  which  is  a  consequence  of 
a  rotation,  on  the  motion  of  the  satellites  which  revolve  around  it. 
These  effects  are  so  small  that  it  is  questionable  whether  accurate 
results  can  be  obtained  by  them  or  not.  Little  is  directly  known 
regarding  the  physical  condition  of  Uranus  except  its  density.  Per- 
haps an  exception  to  this  statement  should  be  made  because,  when. 
the  light  which  is  received  from  it  is  analyzed  by  the  spectroscope, 
it  is  found  that  the  atmosphere  of  Uranus  has  subtracted  some  of  the 
light.  The  part  of  the  light  which  is  absorbed  in  this  way  depends 
upon  the  constitution  of  the  absorbing  gas.  From  a  study  of  its  light, 
made  particularly  at  the  Lowell  Observatory,  it  is  inferred  that 
Uranus  has  an'extensive  atmosphere  made  up  to  a  considerable  degree 
of  light  gases.  It  is  found  from  the  observations  that  Uranus  reflects 
about  60  per  cent  of  the  sunlight  which  falls  upon  it,  and  this  also 
goes  to  support  the  conclusion  that  it  has  an  extensive  cloud-filled 
atmosphere. 

Neptune.  Neptune  is  the  most  remote  planet  from  the  sun,  so 
far  as  is  known,  and  is  most  inconveniently  situated  for  observations 
from  the  earth.  No  surface  markings  on  it  have  been  detected  and 
nothing  is  known  regarding  the  character  of  its  surface  or  the  rate 
of  its  rotation.  From  its  low  mean  density,  high  reflective  power, 
and  the  character  of  the  light  its  atmosphere  absorbs,  it  is  inferred 
that  it  has  surrounding  it  an  extensive  atmosphere  of  light  gases. 
It  has  one  known  satellite  which  revolves  around  the  planet  in  a 
period  of  about  six  days  and  which  has  a  diameter  of  about  2,000 
miles.  The  plane  of  the  satellite's  motion  is  inclined  to  the  plane 
of  the  orbit  of  the  planet  by  35  degrees,  and  it  moves  in  the  retro- 
grade direction.  If  the  satellite  is  in  the  plane  of  the  planet's  equator, 
and  if  the  planet  rotates  in  the  direction  of  the  satellite,  it  is  the  only 
example  known  of  a  planet  rotating  backward. 


182  ASTRONOMY 

The  discovery  of  Neptune,  made  in  1846,  was  the  result  of  one 
of  the  most  brilliant  predictions  ever  made  in  science.  Irregularities 
in  the  motions  of  Uranus  led  to  it.  As  was  explained  in  connection 
with  the  discussion  of  the  planetoids,  the  orbit  of  a  planet  can  be 
found  from  a  few  observations,  and  its  position  thereafter  can  be 
predicted  for  any  length  of  time,  however  great.  After  Herschel 
discovered  Uranus  and  had  made  a  sufficient  number  of  observations 
of  it  to  enable  mathematicians  to  compute  its  orbit,  its  theoretical 
position  was  calculated  for  many  years.  By  1820,  or  40  years  after 
its  discovery,  it  was  found  that  the  planet  was  deviating  a  little  from 
its  predicted  path.  By  1830  the  deviation  was  a  little  greater,  and 
by  that  time  had  become  sufficiently  large  to  seriously  disturb 
astronomers.  This  does  not  mean  that  mathematicians  predicted 
Uranus  would  be  seen  in  one  part  of  the  sky  and  that  it  was  actually 
seen  in  quite  another,  but  that  the  deviation  was  enough  so  that  it 
could  be  observed  with  a  telescope.  As  a  matter  of  fact,  the  planet 
was  actually  observed  so  near  its  theoretical  position  that  the  differ- 
ence was  quite  beyond  the  limits  of  visibility  without  a  telescope. 
That  is,  if  a  star  were  in  the  predicted  place  and  another  in  the 
observed  place,  the  two  would  be  seen  as  one  without  optical  aid. 
The  exactness  of  astronomical  science  is  shown  by  the  fact  that  so 
small  a  disagreement  between  theory  and  observation  as  this  should 
have  caused  astronomers  so  much  unrest. 

The  explanation  of  the  discrepancy  between  theory  and  observa- 
tion was  not  easy  to  make.  However,  shortly  after  1830  a  German 
astronomer,  named  Bessel,  suggested  that  perhaps  Uranus  was 
deflected  from  its  predicted  path  because  of  the  attraction  for  it  of 
an  unknown  planet  situated  out  beyond  it.  The  problem  of  finding 
the  position  of  the  unknown  planet  from  so  slight  an  irregularity  as 
was  observed  in  the  motion  of  Uranus,  was  one  of  immense  difficulty, 
and  one  which  no  one  at  the  time  had  the  courage  to  undertake  to 
solve.  The  matter  rested  for  about  ten  years  and  then  two  young 
men  undertook  the  solution  of  the  problem.  One  was  Adams  of 
Cambridge,  England,  and  the  other,  Leverrier,  of  Paris.  They  began 
work  on  the  problem,  each  entirely  independent  of  the  other,  and 
without  knowledge  that  the  other  was  undertaking  it.  Adams 
finished  his  results  first,  in  1845,  and  found  where  the  unknown 
world  must  be.  He  took  his  figures  to  English  astronomers  who  had 


ASTRONOMY  183 

telescopes  and  asked  them  to  search  for  it.  He  did  not  succeed  in 
arousing  any  particular  interest,  nor  in  having  active  steps  taken  in 
the  search.  Being  somewhat  discouraged  by  the  rebuffs  he  met,  he 
let  the  matter  rest.  In  the  meantime  Leverrier  finished  his  compu- 
tations by  a  different  method,  and  arrived  at  essentially  the  same 
conclusions.  He  sent  the  results  of  his  computations  to  a  young 
German  astronomer  named  Galle.  The  latter  had  the  enthusiasm 
and  the  optimism  of  youth,  and  began  the  search  the  first  night 
after  receiving  the  letter  from  Leverrier.  One  can  imagine  with 
what  impatience  he  waited  for  the  sun  to  set  and  the  stars  to  appear. 
When  it  finally  became  dark  he  turned  his  telescope  to  the  sky  and 
found,  almost  at  the  place  Leverrier  had  predicted,  within  half  an 
hour  after  he  had  begun  his  search,  the  unknown  world.  It  is  distant 
from  the  sun  nearly  3,000,000,000  miles,  and  beyond  all  the  senses 
except  sight,  and  then  can  be  observed  only  with  optical  aid.  It 
had  made  itself  known  only  through  its  effects  on  the  motion  of  the 
planet  Uranus,  which  had  accumulated  for  a  period  of  nearly  70  years. 
It  is  one  of  the  triumphs  of  the  human  intellect  that  these  men 
should  have  been  able,  with  the  instrument  of  analysis,  to  penetrate 
to  such  great  distances  and  find  with  certainty  the  existence  of  a 
world  which  up  to  that  time  had  been  entirely  unknown. 

One  might  raise  the  question  whether  there  are  not  still  other 
planets  farther  out  than  Neptune.  If  there  are,  in  the  course  of 
time  they  will  make  themselves  felt  by  the  disturbance  of  the  motion 
of  the  planet  Neptune.  But  since  Neptune  revolves  around  the  sun 
only  once  in  165  years,  it  is  clear  that  a  very  long  time  might  elapse 
before  they  both  came  on  the  same  side  of  the  sun  where  these 
disturbing  effects  would  be  the  greatest.  Only  66  years  have  passed 
since  the  discovery  of  Neptune,  and  consequently  the  chances  are 
rather  against  it  having  come  in  conjunction  with  any  other  planet 
farther  out.  At  the  present  time  there  is  no  certain  evidence  of  any 
disturbance  in  the  motion  of  Neptune  which  can  not  be  explained 
by  the  action  of  the  planets  so  far  known.  On  the  other  hand, 
there  is  no  particular  reason  to  suppose  that  there  may  not  be  other 
planets  farther  from  the  sun. 


THE    GREAT    MOREHOUSE    COMET 
Picture  taken  October  30,  1908 


ASTRONOMY 

PART  IV 


COMETS  AND  METEORS 

Orbits  of  Comets.  Comets  are  wandering  bodies  which  pass 
around  the  sun,  usually  in  sensibly  parabolic  orbits.  (See  Fig.  67.) 
If  their  orbits  are  exactly  parabolas  it  means  they  have  come  in 
from  the  sun  from  an  infinite  distance,  and  will  go  out  again  to  an 
infinite  distance,  never  to  return.  It  is  not  possible  to  say  that  in 
any  case  the  orbit  is  exactly  a  parabola,  because  the  observations 
are  made  for  only  a  short  time  while  the  comet  is  nearest  the  sun. 
It  is  clear  from  the  common  sense  of  the  situation  that  under  these 
circumstances  the  whole  extent  of  the  orbit  can  not  be  determined 
with  perfect  accuracy.  A  very  slight  error  in  an  observation,  which 
would  make  no  sensible  difference  in  the  part  of  the  orbit  near  the 
sun,  might  make  a  very  great  difference  in  the  remote  part.  It  is 
similar  to  the  problem  of  determining  a  circle  by  means  of  three 
points.  It  is  known  from  geometry  that  if  three  points  not  in  a 
straight  line  are  given,  the  circle  through  them  is  determined.  If 
the  three  points  are  very  near  together  the  circle  is  poorly  deter- 
mined, especially  in  the  parts  remote  from  the  three  points. 

While  the  statement  is  true  that  the  great  majority  of  comets 
move  in  sensibly  parabolic  orbits,  and  that  it  is  not  certain  that 
they  move  in  exactly  parabolic  orbits,  there  are  certainly  some  which 
move  in  elliptical  orbits.  These  comets  come  in  from  finite,  though 
in  some  cases  great,  distances  and  go  out  again  to  the  same  distances. 
They  return  to  the  sun  time  after  time,  their  periods  of  revolution 
depending  upon  the  lengths  of  their  orbits.  There  are  a  very  few 
cases  in  which  it  seems  that  comets  move  in  hyperbolic  orbits, 
though  there  is  some  room  for  doubt  regarding  the  conclusion. 

If  the  comets,  as  a  whole,  move  in  parabolic  orbits  they  can  not 
be  considered  as  permanent  members  of  the  solar  system.  On  the 
other  hand,  if  their  orbits,  instead  of  being  parabolas,  are  very 

Copyright,  1912,  by  American  School  of  Correspondence. 


186  ASTRONOMY 

elongated  ellipses  they  are  permanent  members  of  the  system.  The 
opinion  seems  to  be  growing  among  astronomers  that  t;he  comets 
are  actually  in  this  sense  permanent  members  of  the  solar  system, 
though  no  rigorous  proof  of  the  statement  is  at  present  at  hand. 
It  has  been  seen  that  the  orbits  of  the  planets  are  all  nearly  in  the 
same  plane  and  that  the  planets  revolve  around  the  sun  in  the  same 
direction.  In  the  case  of  comets  it  is  quite  different.  Their  orbits 
lie  in  every  plane  and  they  revolve  in  all  directions.  There  is  no 
uniformity  in  their  distribution.  The  only  thing  that  can  be  said  is 
that  there  is  a  tendency  for  the  perihelia  of  comet  orbits  to  cluster 
on  the  side  of  the  sun  which  is  ahead  in  its  motion  through  space. 

Dimensions  and  Masses  of  Comets.  Comets  consist  of  a  head 
containing  in  it,  usually,  a  small  bright  nucleus,  and  a  long  tail 
streaming  out  in  the  direction  opposite  to  the  sun.  The  head  may 
vary  anywhere  from  10,000  miles  up  to  more  than  1,000,000  miles. 
The  nucleus  is  generally  a  few  hundred,  and  at  the  most  a  few 
thousand,  miles  in  diameter.  The  tails  are  in  length  from  a  few 
millions  up  to  more  than  100,000,000  miles. 

A  remarkable  thing  about  the  head  of  a  comet  is  that  it  nearly 
always  contracts  as  the  comet  approaches  the  sun,  and  expands 
again  when  it  recedes.  On  the  contrary  the  tail  increases  enormously 
when  the  comet  approaches  the  sun,  and  diminishes  as  it  recedes. 
The  nuclei  of  comets  vary  in  size,  but  in  an  irregular  fashion  for 
which  no  law  has  been  discovered. 

The  fact  that  the  tails  of  comets  point  away  from  the  sun  is 
a  matter  of  the  highest  interest.  It  is  not  very  easy  to  explain 
precisely  the  reasons  for  this.  One  of  the  chief  hypotheses  so  far 
advanced  for  explaining  this  phenomenon  is  that  the  sun  exerts  an 
electrical  repulsion  on  the  particles  which  come  from  the  head  and 
go  off  in  space  to  form  the  tail.  More  recently  it  has  been  found 
both  theoretically  and  experimentally  that  light  exerts  a  pressure 
which  depends  upon  its  intensity  and  upon  the  surface  of  the  body  on 
which  it  falls.  Light  pressure  is  so  feeble  a  force  that  it  does  not  sen- 
sibly affect  masses  of  large  dimensions,  but  it  can  be  an  appreciable 
disturbing  influence  in  very  small  particles.  The  general  conclusion 
at  present  is  that  the  tails  are  produced  by  electrical  disturbances 
and  that  they  project  out  from  the  heads  of  comets  in  the  direction 
opposite  to  the  sun  because  of  electrical  repulsion  and  light  pressure. 


ASTRONOMY  187 

Comets  shine  both  by  reflected  light  and  by  their  own  intrinsic 
brilliance.  -When  they  are  far  from  the  sun,  i.  e.,  beyond  the  orbit 
of  Mars,  they  are  generally  very  faint  and  shine  almost  entirely  by 
reflected  light.  As  they  approach  the  sun  they  become  active 
internally  and  increase  in  brightness,  not  only  because  they  are 
more  brightly  illuminated  by  the  sun,  but  also  because  they  become 
self-luminous  in  some  way  which  is  not  fully  understood. 

Notwithstanding  the  fact  that  the  volume  of  a  comet  is  often 
very  great,  exceeding  that  of  all  the  planets  of  the  system  and  even 
that  of  the  sun  itself,  yet  comet  masses  are  very  small.  This  is 
proved  by  the  fact  that  when  they  pass  near  planets,  the  planets 
pull  them  entirely  from  their  paths  by  their  attractions,  while  the 
comets  do  not  in  turn  disturb  the  planets  enough  so  that  it  can  be 
observed.  In  fact,  one  comet  passed  through  Jupiter's  satellite 
system  in  1886.  This  great  planet  and  its  satellites  totally  changed 
the  orbit  of  the  comet,  but  it  in  turn  did  not  disturb  even  one  of  the 
satellites  enough  so  that  the  changes  in  its  motion  could  be  observed. 
From  these  facts,  chiefly,  we  infer  the  very  small  masses  of  the 
comets. 

As  a  comet  moves  around  the  sun  its  mass  is  continually  dis- 
sipated in  space  along  its  tail,  as  is  illustrated  in  Fig.  87.  The  light, 
volatile  materials  held  in  its  head  and  nucleus  are  evolved  under 
the  stimulus  of  the  sun's  heat  and  electrical  activity,  and  are  repelled 
out  into  space,  never  to  return  to  it  again.  In  the  case  of  comets 
which  move  around  the  sun  in  closed  orbits,  this  dissipation  of  material 
continues  until  they  often  become  altogether  invisible.  There  are  now 
numerous  examples  of  comets  whose  light  has  failed,  apparently 
because  of  the  dissipation  of  their  luminous  parts  into  space. 

Capture  of  Comets.  Suppose  a  comet  comes  into  the  solar 
system  on  a  very  elongated  orbit,  perhaps  a  parabola.  If  it  does 
not  pass  near  a  planet  it  will  go  around  the  sun  and  out  again  on 
a  curve  of  the  same  character.  If  it  passes  near  a  planet  the  orbit 
may  be  entirely  changed,  and  the  character  of  this  change  depends 
upon  the  circumstances  of  the  near  approach  to  the  planet.  Under 
certain  circumstances  the  orbit  will  be  reduced  from  an  elongated 
one  to  one  which  is  more  nearly  circular.  In  this  manner  a  parabolic 
orbit  may  be  reduced  to  an  elliptical  one.  Jupiter,  having  a  greater  . 
mass  than  any  other  planet  and  in  fact  greater  than  all  of  them 


Fig.  87. 


Matter  Receding  from  the  Head  of  a  Comet  and  Forming  a  Long  Tail.     Photo- 
graphed by  Barnard 


ASTRONOMY 


189 


combined,  obviously  will  capture  more  comets  than  any  other  planet. 
Its  chances  are  favorable  also  because  of  its  location.  If  a  planet 
beyond  Jupiter  should  capture  a  comet,  this  orbit  would  still  pass 
that  of  Jupiter  and  Jupiter  in  turn  might  capture  it  and  reduce  its 
orbit  still  further.  But  if  Jupiter  reduced  the  orbit  of  a  comet  so 
that  its  aphelion  point  were  at  approximately  the  distance  of  this 
planet,  the  planets  farther  out  would  thereafter  have  no  sensible 
effect  upon  it.  For  these  reasons  Jupiter  has  a  larger  family  of 


The  Orbits  of  Comets  Which  Have  Been  Captured  by  Jupiter 


captured  comets  than  any  other  planet.  In  Fig.  88  the  small  circle 
represents  the  orbit  of  the  earth  and  the  large  circle  the  orbit  of 
Jupiter.  The  ellipses  are  the  orbits  of  those  comets  which  belong  to 
Jupiter's  family.  Some  of  them  have  now  become  invisible  because 
of  the  dissipation  of  their  material  in  space. 

The  planets  Uranus  and  Neptune  have  small  comet  families, 
and  there  are  other  comets  whose  aphelia  are  still  farther  from  the 
sun.  Perhaps  this  may  be  considered  as  a  reason  for  suspecting  the 
existence  of  planets  farther  out  than  Neptune.  The  members  of 
one  small  group  of  comets  at  their  most  remote  distances,  are  about 
three  times  as  far  from  the  sun  as  Neptune  is,  and  the  other  about 


190  ASTRONOMY 

ten  times  as  far  Planets  at  those  distances  would  revolve  around 
the  sun  in  the  immense  periods  of  1,000  and  5,000  years  respectively. 

Celebrated  Comets.  Among  the  celebrated  comets  of  historical 
times  that  of  1680  may  be  mentioned  as  being  the  one  to  which 
Newton's  theory  of  gravitation  was  first  applied.  Its  orbit  was 
computed  and  it  was  found  that  it  revolved  in  a  long  ellipse  with 
a  period  of  about  600  years.  At  its  nearest  approach  to  the  sun  it 
was  only  140,000  miles  from  the  sun's  surface,  and  it  moved  at  the 
rate  of  370  miles  per  second.  Its  tail,  when  it  was  near  the  sun,  was 
100,000,000  miles  in  length. 

Halley's  comet  is  another  one  of  the  important  historical  comets. 
It  appeared  in  1682,  four  years  before  Newton's  publication  of  the 
law  of  gravitation.  After  the  work  of  Newton  appeared  his  friend, 
Edmund  Halley,  applied  his  method  to  the  computation  of  the 
orbit  of  this  comet.  He  found  that  it  was  almost  identical  with  that 
of  the  comets  of  1607  and  1531.  He  came  to  the  conclusion  that 
these  various  comets  were  but  different  appearances  of  the  same 
one,  which  revolved  around  the  sun  in  a  period  of  about  75  years, 
there  being  slight  deviations  from  this  number  owing  to  the  attrac- 
tions of  the  planets.  Going  back  in  the  historical  records,  it  was 
found  that  comets  had  been  observed  at  intervals  of  about  75  years, 
reaching  back  to  a  century  or  so  before  the  beginning  of  the  Chris- 
tian era.  There  is  little  doubt  that  Halley's  comet  has  been  observed 
during  twenty- five  of  its  approaches  to  the  sun.  Halley  confidently 
predicted  that  the  comet  would  reappear  and  pass  its  perihelion  on 
March  13, 1759.  He  recognized  the  fact  that  the  perturbations  of  the 
planets  and  the  uncertainties  in  its  orbit  might  make  his  predictions  of 
the  time  of  its  next  approach  to  the  sun  slightly  inexact.  This  was  the 
first  long  range  scientific  prophecy.  It  was  made  in  precise  mathe- 
matical terms  without  the  use  of  ambiguous  language.  The  ful- 
fillment or  failure  of -it  was  awaited  with  great  interest  as  the  time 
drew  near.  When  the  year  1759  came  the  comet  reappeared  accord- 
ing to  the  predictions  of  Halley  and  passed  the  sun  within  a  month 
of  the  time  he  considered  most  probable.  Before  that  time  there  was 
no  prophecy  in  all  history  made  in  so  definite  terms  which  was  so 
literally  fulfilled. 

Halley's  comet  appeared  again  in  1835,  when  it  passed  within 
5,000,000  miles  of  the  earth.  Fig.  89  shows  the  position  of  the  orbit 


ASTRONOMY 


191 


with  respect  to  the  earth's  orbit  and  that  of  Neptune.  After  its 
appearance  in  1835  it  went  out  into  space  and  quickly  became  invisi- 
ble. For  almost  75  years  it  was  beyond  the  range  of  even  the  most 
powerful  instruments,  and  was  followed  in  its  course  only  by  mathe- 
matical processes.  Though  it  could  not  be  seen  and  its  existence 
and  position  could  not  be  proved  by  any  direct  processes,  yet  the 
perfection  of  astronomical  theory  is  so  great  that  those  best  qualified 
to  judge  never  doubted  for  a  moment  that  the  theory  indicated 
exactly  where  it  was.  It  was  known  from  the  computations  that 
it  would  appear  again  in  1910.  The  event  is  of  so  recent  occurrence 
that  everybody  knows  of  its  return,  and  that  it  passed  the  sun  in 
perfect  harmony  with  the  predictions.  The  newspaper  tales  of  the 
mysteries  and  peculiarities  attached  to  it  were  pure  fiction. 


Fig.  89.     The  Orbit  of  Halley's  Comet 

Fig.  90  shows  the  relative  positions  of  the  comet  and  the  earth 
during  its  time  of  nearest  approach  to  the  sun  and  the  earth.  On 
April  19  the  comet  was  at  its  nearest  approach  to  the  suri,  but  was 
so  far  from  the  earth  that  it  was  not  a  very  conspicuous  object.  On 
May  18  it  passed  between  the  earth  and  the  sun  and  at  this  time  was 
visible.  Between  the  latter  part  of  March  and  May  18  it  was  visible 
in  the  morning  sky.  After  May  18  it  became  visible  in  the  evening 
sky.  The  diagram,  taking  into  account  the  direction  of  the  motion 
of  the  earth  and  of  its  rotation,  will  show  the  reasons  for  this. 

Encke's  comet,  discovered  in  1819,  is  remarkable  for  the  fact 
that  it  has  the  shortest  known  period  (3.3  years),  and  also  for  the 
fact  that  its  period  was  shortened  during  several  revolutions  without 
any  known  reason.  It  has  been  suggested  that  it  was  due  to  its 
encountering  some  resisting  matter  in  the  system,  and  that  is  prob- 
ably the  true  explanation. 

Biela's  comet,  discovered  in  1826,  revolves  around  the  sun  in 
a  period  of  6.6  years  and  is  remarkable  particularly  for  the  fact  that 


192 


ASTRONOMY 


in  1847  it  broke  into  two  parts  which  gradually  separated.    Since 
1852  it  has  not  been  observed. 

The  great  comets  of  1880  and  1882  were  remarkable  for  their 
splendor,  for  the  nearness  of  their  approach  to  the  sun,  and  for 
the  fact  that  they  moved  in  almost  the  same  orbit.  The  orbits  of 
these  comets  are  very  elongated  and  their  period  of  revolution,  if 
indeed  their  orbits  are  elliptical,  must  be  several  hundred  years 


Fig.  90.     Path  of  Halley'a  Comet  Showing  nearest  Approach  to  Earth 

Consequently,  the  two  objects  can  not  have  been  the  same  one.  They 
were  simply  two  bodies  moving  in  almost  the  same  paths.  Other 
comets  moving  in  the  same  orbit,  at  least  approximately,  were 
those  of  1668  and  1843,  both  of  which  were  brilliant  objects.  These 
comets  either  have  had  a  similar  origin,  or  are  fragments  of  a  once 
greater  comet  which  has  been  broken  into  a  number  of  pieces  in  some 
transit  through  the  solar  system. 

Meteors  or  Shooting  Stars.  An  attentive  watch  of  the  sky  on 
almost  any  clear  evening  for  a  little  while  will  show  one  or  more 
so-called  shooting  stars.  They  are  little  flashes  of  light  which  have 


ASTRONOMY  193 

the  appearance  of  being  a  star  darting  across  the  sky  and  disappear- 
ing. Since  to  call  them  shooting  stars  is  a  little  misleading,  we  shall 
always  speak  of  them  as  meteors.  Instead  of  being  actual  stars, 
they  are  as  a  matter  of  fact  tiny  masses  of  matter,  so  small  that  one 
could  hold  them  in  his  hand,  which  are  moving  in  space  in  the  vicinity 
of  the  earth.  Under  certain  circumstances  of  motion  and  position 
they  dash  into  the  earth's  atmosphere  with  a  velocity  which  usually 
lies  between  10  and  40  miles  per  second.  The  heat  generated  by 
friction  with  the  air  of  bodies  moving  with  this  high  speed  burns  them 
up.  The  products  of  their  combustion  and  pulverization  fall  to  the 
earth,  or  are  added  to  the  atmosphere. 

The  height  of  meteors  is  obtained  from  observations  of  them  at 
two  different  places.  These  observations  at  the  same  time  give  the 
lengths  of  their  luminous  paths.  If  their  brightness  is  also  measured 
and  the  time  which  they  are  visible,  it  is  possible  to  compute  the 
whole  amount  of  light  which  they  radiate.  This  radiant  energy 
depends  upon  the  mass  of  meteorite  and  its  velocity.  The  velocity 
being  known,  the  mass  remains  the  only  unknown  and  can  be  com- 
puted. It  is  in  this  way  that  it  has  been  found  that  the  masses  of 
meteors  are  very  small,  usually  being  only  a  few  grains. 

The  numbers  of  meteors  are  much  greater  than  one  might 
imagine  when  he  finds  that  generally  he  can  see  only  a  few  in  watch- 
ing an  hour.  The  reasons  are  that  he  can  not  see  the  whole  visible 
sky  at  one  time,  and  that  only  a  small  part  of  the  earth's  atmosphere 
is  within  the  range  of  his  vision  at  one.  time.  If  a  circle  is  made  to 
represent  the  earth  and  the  atmosphere  is  put  on  it  to  scale,  it  will 
be  clear  why  an  observer  can  see  so  small  a  part  at  once.  Accurate 
count  of  the  numbers  of  meteors  visible  in  a  given  time,  made  by 
many  observers,  and  computations  to  extend  the  numbers  so  as  to 
include  all  that  fall  on  the  whole  earth,  show  that  from  10,000,000 
to  20,000,000  strike  into  the  earth's  atmosphere  daily. 

Meteors  strike  into  the  earth's  atmosphere  from  every  direc- 
tion, but  more  are  received  on  the  side  of  the  earth  which  is  ahead 
in  its  motion  around  the  sun  than  on  the  side  which  is  behind,  for 
the  side  which  is  ahead  receives  not  only  those  which  meet  the  earth 
but  also  those  which  the  earth  overtakes,  while  the  part  behind 
receives  only  those  which  overtake  the  earth.  It  is  found  that  those 
on  the  side  ahead  strike  with  greater  velocities  than  those  received 


194  ASTRONOMY 

on  the  part  behind,  as  would,  of  course,  be  expected  from  the  nature 

of  the  case. 

The  part  of  the  earth  which  is  ahead  is  that  which  is  on  the 

morning  side  of  the  earth.       In  Fig.  91  let  8  represent  the  sun,  E 

the  earth,  and  the  arrows  the  direction 
of  rotation  and  revolution  of  the  earth. 
The  point  0  is  at  the  sunrise  line  and  is 
on  the  side  of  the  earth  which  is  ahead  in 
its  motion  around  the  sun. 

Relation  of  Comets  and  Meteors.  As 
the  volatile  matter  which  goes  to  make 
up  the  tails  of  comets  is  dissipated  in 
space,  there  is  left  behind  only  the 

Fig.  91.     The  Earth  Encountering  J 

MeteArroindItt8h?esVu°nUtion          denser    particles    which    make    up    the 
head,   or   perhaps   the   nucleus.    These 

denser  particles  continue  to  revolve  around  the  sun  indefinitely 
unless  the  planets  disturb  their  orbits  so  that  they  recede  to 
infinite  distances,  which  is  a  possible  occurrence,  or  unless  they 
are  swept  up  by  the  planets.  If  a  planet  should  strike  the  remains 
of  an  extinct  comet  it  would  encounter  a  swarm  of  particles  moving 
in  sensibly  parallel  directions  and  with  equal  speed.  If  these  par- 
ticles were  small  they  would  produce  a  meteoric  shower. 

Observations  show  that  there  are  many  meteoric  showers. 
Particles  moving  in  sensibly  parallel  lines  strike  into  the  atmosphere 
at  various  times  of  the  year.  In  some  cases  the  orbits  of  these 
particles  around  the  sun  have  been  determined.  One  of  the  most 
celebrated  known  cases,  and  one  which  has  given  the  most  remark- 
able meteoric  showers,  is  that  of  the  meteors  which  the  earth  encoun- 
ters on  November  14.  They  move  in  an  elongated  orbit  of  which 
they  make  the  circuit  once  in  33  years.  They  have  been  moving 
so  long  in  the  orbit  that  they  are  scattered  more  or  less  thickly  along 
its  whole  length,  but  they  are  more  numerous  at  a  certain  place 
than  elsewhere.  Once  in  33  years  the  earth  passes  through  this 
nucleus.  The  swarm  of  meteors  and  the  earth  move  in  opposite 
directions,  and  consequently  the  earth  meets  these  meteors  on  its 
morning  side.  They  appear  to  come  out  of  the  constellation  Leo, 
and  are  hence  called  Leonids.  They  are  almost  certainly  the  remains 
of  a  comet  which  was  captured  by  the  planet  Uranus  in  126  A.  D. 


ASTRONOMY  195 

*This  conclusion  is  based  on  the  computation  of  the  present  position 
of  their  orbit  and  tracing  it  back  until  it  was  found  that  at  this  date 
the  meteors  and  Uranus  were  very  close  together,  and  in  such  a 
relative  position  that  Uranus  would  reduce  their  orbit  from  a  parab- 
ola to  an  elongated  ellipse  in  which  the  comet  would  move  in  a  period 
of  33  years. 

In  1833  the  first  known  remarkable  encounter  with  this  swarm 
was  experienced.  Then,  as  seen  from  some  places,  the  sky  was  filled 
with  thousands  of  meteors.  At  that  time  the  explanation  of  a 
meteoric  shower  was  not  known.  But  in  1866,  on  the  same  day  of 
the  same  month,  a  similar  meteoric  shower  was  observed.  Follow- 
ing this  the  theory  of  the  phenomenon  was  fully  worked  out. 

There  are  many  meteoric  showers,  though  they  are  on  the  whole 
less  conspicuous  than  the  Leonids.  There  is  a  shower  visible  yearly 
on  November  24,  in  the  constellation  Andromeda,  and  other  con- 
spicuous ones  occur  on  April  20  and  about  the  10th  of  August.  It  is 
supposed  that  all  these  meteoric  showers  are  produced  from  the 
remains  of  disintegrated  comets.  If  so,  we  see  how  slight  the 
masses  of  the  comets  are,  and  how  little  we  should  have  to  fear 
even  though  one  were  headed  toward  the  earth  and  a  collision  were 
certain. 

Influences  of  Meteors  on  the  Earth.  It  might  be  supposed 
that  objects  so  small  as  meteors  would  have  no  sensible  effect  on  a 
great  body  like  the  earth,  and  such  is  the  case  if  only  a  short  period 
of  time  is  under  consideration.  But  in  astronomical  and  geological 
science  the  earth  is  considered  not  only  for  years  and  centuries,  but 
for  millions  of  years.  Though  the  effects  of  meteors  are  insensible 
for  years  or  even  centuries,  it  may  be  that  in  the  long  run  they  are 
very  important.  Sometimes  those  influences  which,  though  small, 
work  continually  in  one  direction  are  the  most  important.  For 
example,  the  washing  down  of  mountains  and  hills  and  plateaus 
by  running  water  is  not  a  matter  of  any  consequence  for  a  short 
time,  but  when  considered  during  the  vast  ages  of  the  geological 
changes  this  is  one  of  the  most  important  agencies  in  transforming 
the  earth. 

One  effect  of  meteoric  matter  circulating  around  the  sun  is  to 
resist  the  motion  of  the  earth  a  little.  This  resistance  has  a  slight 
tendency  to  decrease  the  size  of  its  orbit  and  to  bring  it  nearer  and 


196  ASTRONOMY 

nearer  to  the  sun.    In  a  similar  manner  the  resistance  also  slightly 
retards  the  rotation  of  the  earth  and  thus  makes  the  day  longer. 

Another  effect  of  the  sweeping  up  of  meteoric  matter  by  the 
earth  is  that  the  earth's  mass  in  this  manner  continually  grows.  It 
is  conceivable  that  the  earth  has  been  revolving  around  the  sun 
long  enough  to  make  this  a  very  important  factor  in  its  evolution, 
and  it  is  also  conceivable  that  in  former  times  the  rate  at  which 
meteoric  matter  was  acquired  was  much  faster  than  at  the  present 
time.  An  indirect  effect  of  the  growth  of  the  earth  is  that  because 
of  its  greater  gravitative  power  it  slowly  though  slightly  winds  in 
toward  the  sun.  No  calculations  are  at  hand  which  enable  us  to 
give  any  precise  estimate  of  the  effects  of  these  causes  upon  the 
evolution  of  the  earth. 

Meteorites.  Now  and  then  large  bodies,  weighing  from  a  few 
pounds  up  to  a  few  tons,  dash  into  our  atmosphere  and  plunge  down 
through  it  in  a  few  seconds  and  strike  the  surface  of  the  earth  with 
great  violence.  Those  bodies  whose  masses  are  so  great  and  which 
are  solid  enough  to  last  until  they  strike  the  surface  of  the  earth, 
are  called  meteorites  in  contrast  to  those  which  are  burned  up  in  the 
atmosphere  and  which  are  known  as  meteors.  The  meteorites  are 
generally  composed  largely  of  rocky  material,  though  they  are  often 
mixed  with  some  metallic  iron.  When  pure  iron  is  not  found  its 
compounds  are  usually  present.  About  three  or  four  per  cent  of 
the  meteorites  which  fall  are  almost  pure  iron  mixed  with  a  little 
nickel.  Altogether  about  thirty  of  the  eighty  elements  known  on 
the  earth  have  been  found  in  meteorites,  but  no  new  substances. 
Yet  the  structure  of  meteorites  is  quite  different  in  some  cases  from 
that  of  any  minerals  found  on  the  earth,  and  from  an  examination 
of  them  it  can  be  proved  that  they  are  of  extra-terrestrial  origin. 

Some  meteorites  show  evidences  of  remarkably  perfect  crystal- 
lization; others  show  places  where  they  have  sometime  been  frac- 
tured and  later  cemented.  Sometimes  at  the  fractured  place  one 
part  has  slipped  slightly  on  another  before  they  were  again  joined 
in  a  solid  mass.  These  facts  are  very  important  in  connection  with 
theories  regarding  their  origin.  The  very  perfect  crystallization, 
as  well  as  the  fractures  and  re-cementation,  indicate  strongly  that 
these  bodies  are  fragments  of  large  masses  of  world-like  dimensions. 
If  so,  they  are  not  masses  ejected  from  the  sun  or  by  volcanoes  from 


ASTRONOMY  197 

the  earth  and  moon,  for  in  those  cases  they  would  cool  quickly  and 
be  glassy  rather  than  crystalline,  and  there  would  be  no  chance  for 
fractures  and  re-cementation.  Chamberlin  has  suggested  that 
probably  they  are  fragments  of  planets  which  once  existed  before 
the  origin  of  our  present  system. 

THE  SUN 

Light  and  Heat  Received  from  the  Sun.  It  is  a  matter  of  com- 
mon observation  that  the  sun  furnishes  the  earth  an  enormous 
amount  of  light.  Compared  to  full  sunlight,  almost  any  artificial 
light  used  for  illumination  seems  dull  ard  feeble.  Even  when  the 
sun's  rays  are  largely  cut  off  by  clouds,  the  illumination  of  a  room 
or  building  is  generally  much  greater  than  it  is  at  night  with  the 
artificial  lights  which  are  ordinarily  used.  A  direct  measurement  of 
the  intensity  of  sunlight  shows  that  it  is  60,000  times  that  of  a 
standard  candle  at  a  distance  of  one  yard. 

Light  is  a  wave  motion  in  the  ether  in  many  respects  similar 
to  sound  waves  in  the  air,  though  there  are  some  fundamental  differ- 
ences. Sound  waves  to  which  the  ear  is  sensitive  vary  in  length 
from  approximately  an  inch  to  many  feet.  Light  waves  to  which 
the  eye  is  sensitive  vary  in  length  from  about  3-5-,  WT  of  an  inch  for 
the  red  to  about  T^/O  i>  of  an  inch  for  the  violet.  The  longest  waves 
are  less  than  twice  as  long  as  the  shortest  ones.  In  the  terminology 
of  acoustics,  our  eyes  are  sensitive  to  less  than  one  octave  of  light, 
while  our  ears  are  sensitive  to  ten  octaves  of  sound.  There  are  vibra- 
tions in  the  ether  shorter  than  violet  rays  and  others  much  longer. 
Those  which  are  shorter  than  the  violet  rays  are  known  as  the  ultra- 
violet, or  chemical,  rays,  and  those  which  are  longer  than  the  red 
rays  are  known  as  the  infra-red)  or  heat,  rays.  From  the  standpoint 
of  physics  all  of  these  rays  are  similar,  and  for  short  we  may  term 
them  altogether  radiant  energy.  The  heat  waves  raise  the  tem- 
perature of  a  dark  object  on  which  they  fall,  and  so  also  do  both  the 
light  waves  and  the  chemical  waves.  It  follows  that  in  considering 
the  light  and  heat  received  from  the  sun  we  may  group  all  of  it 
together  and  treat  it  as  a  single  type  of  energy. 

It  is  possible  to  measure  directly  the  radiant  energy  received 
from  the  sun  at  the  earth's  surface.     The  difficulty  in  measuring 


198  ASTRONOMY 

how  much  is  actually  received  by  the  earth  arises  from  the  fact  that 
it  is  hard  to  determine  how  much  is  absorbed  in  passing  through  the 
atmosphere.  But  by  making  observations  at  the  sea  level  and  again 
on  high  mountains,  and  taking  into  account  the  difference  in  the 
amount  of  air  which  the  energy  has  passed  through  at  the  two  posi- 
tions, it  is  possible  to  get  a  tolerably  accurate  estimate  of  the  absorb- 
ing effects  of  the  atmosphere.  In  describing  the  energy  received 
from  the  sun  we  may  express  the  quantity  in  various  units,  as  for 
example,  the  calory  used  by  engineers,  or  the  horse-power,  which  is 
in  more  common  use.  Everyone  is  familiar  with  the  fact  that  heat 
energy  is  equivalent  to  work,  and  an  example  of  its  transformation  is 
in  the  steam  engine  where  the  heat,  generating  steam,  does  work  by 
means  of  the  steam  engine.  The  unit  of  work  known  as  the  horse- 
power will  raise  33,000  pounds  one  foot  high  in  one  minute.  Obser- 
vations show  that  the  radiant  energy  received  from  the  sun  on  every 
square  yard  exposed  perpendicularly  to  its  rays  is  equivalent  to 
three  horse-power.  The  earth's  surface  is  four  times  the  area  of  a 
circle  whose  diameter  is  equal  to  that  of  the  earth,  and  consequently 
the  average  amount  of  energy  received  per  square  yard  on  the  whole 
earth's  surface  is  three-fourths  of  a  horse-power.  It  follows  from 
this  that,  if  the  energy  which  falls  from  the  sun  on  a  manufactory 
could  be  used  for  mechanical  purposes,  it  would  run  all  the  machin- 
ery within  it.  But  it  is  not  possible  to  use  more  than  a  very  small 
fraction  of  the  sun's  energy  for  the  purpose  of  doing  work. 

Notwithstanding  the  fact  that  the  sun's  energy  is  not  directly 
available  as  a  source  of  power,  it  is  worthy  of  note  that  almost  all  the 
energy  which  we  use  has  been  derived  indirectly  from  the  sun.  A 
former  important  source  of  energy  was  the  wind  which  drove  thou- 
sands and  thousands  of  windmills,  and  pushed  boats  over  the  seas. 
The  energy  of  the  winds  is  entirely  due  to  the  sun.  The  winds  blow 
because  the  sun  heats  up  the  equatorial  zone  of  the  earth  more  than 
it  does  the  higher  latitudes. 

Another  source  of  energy  which  was  formerly  more  important 
relatively  than  it  is  at  present,  was  the  water  power.  The  energy  given 
up  by  the  waterfall  was  indirectly  derived  from  the  sun;  the  sun's 
heat  raised  the  water  in  the  form  of  vapor  from  the  oceans  and  lower 
levels  into  the  atmosphere,  and  the  winds  carried  it  in  many  cases 
thousands  of  miles  out  over  the  land  where  it  fell  as  rain  or  snow  on 


ASTRONOMY  199 

the  mountains  and  in  the  higher  altitudes.  Running  down  from 
the  higher  places  and  uniting  into  rivers,  it  became  a  practical 
source  of  energy  where  it  plunged  over  precipices.  The  original  rain 
may  have  fallen  from  an  altitude  of  a  half-mile  or  a  mile,  while  in 
the  waterfall  we  generally  use  a  fall  of  not  many  feet,  and  in  extreme 
cases  not  more  than  a  hundred  or  so.  It  is  obvious  from  this  how 
small  a  fraction  of  the  energy  of  the  falling  water  could  be  utilized 
even  if  every  waterfall  in  the  world  were  used  to  the  extreme  limit. 

The  amount  of  energy  in  the  falling  water  can  be  seen  from 
the  number  of  tons  which  descend  in  a  heavy  rain.  While  an  inch  of 
water  is  a  very  heavy  rain,  yet  this  amount  often  falls  in  a  few  hours. 
Since  the  weight  of  a  cubic  foot  of  water  is  62J  pounds,  a  little  com- 
putation shows  that,  in  an  inch  of  rain  on  a  square  mile,  more  than 
60,000  tons  fall  from  the  sky  to  the  earth.  In  a  large  part  of  the 
United  States  the  annual  rainfall  is  about  30  inches,  or  in  round 
numbers  2,000,000  tons  per  square  mile.  Remembering  that  in 
North  America  alone  there  is  a  territory  of  at  least  1,500  miles  square 
where  the  average  rainfall  is  about  2,000,000  tons  per  square  mile, 
one  gets  an  idea  of  the  enormous  energy  the  sun  has  put  forth  in 
evaporating  the  water  of  the  oceans  and  raising  it  into  the  air. 
Clearly,  this  is  an  extremely  small  fraction  of  the  solar  energy  which 
falls  on  the  earth. 

The  most  important  source  of  energy  at  the  present  time  for 
mechanical  purposes  is  undoubtedly  coal.  The  coal  had  its  origin 
in  plant  life  which  flourished  ages  ago.  Consequently,  the  energy 
which  the  coal  gives  off  when  consumed  in  our  furnaces,  was  origi- 
nally derived  from  plants.  Now,  the  plants  get  their  energy  from 
the  sun.  The  little  cells  in  the  leaves  and  stems  are  minute  labora- 
tories where  the  sun  does  work  and  where  its  energy  is  stored  up.  It 
is,  of  course,  true  that  the  plants  live  to  some  extent  on  the  earth  and 
water,  but  an  examination  of  their  constitution  shows  that  it  is  a 
fact  that  almost  all  the  energy  which  is  stored  up  in  their  fibers  has 
been  derived  from  the  sun.  Consequently,  when  one  sees  a  rail- 
way train  driven  by  the  coal  which  is  fed  into  its  furnace,  he  is  seeing 
it  pushed  indirectly  by  energy  derived  from  the  sun.  It  follows 
from  the  fact  that  the  plants  receive  their  energy  almost  entirely 
from  the  sun  that  the  animals,  which  live  upon  plants,  receive  their 
energy  almost  entirely  from  the  sun.  As  a  matter  of  fact,  almost  all 


200  ASTRONOMY 

the  motions  and  activities  which  come  under  our  observation,  except 
the  motions  of  the  heavenly  bodies  themselves,  are  due  to  energy 
derived  from  the  sun. 

The  earth,  as  seen  from  the  sun,  would  be  a  very  small  point  in 
the  sky,  about  as  large  as  Mars  appears  from  the  earth.  The  sun 
radiates  heat  and  light  into  space  in  every  direction.  Consequently 
it  follows  that  the  amount  of  light  and  heat  received  by  the  earth 
from  the  sun  is  only  a  very  small  fraction  of  the  whole  amount 
radiated.  It  is  approximately  T,o"o~o,innr,¥iro  of  the  energy  poured 
out  by  the  sun.  This  means  that  the  sun's  surface  is  radiating  heat 
and  light  at  an  enormous  rate.  The  computation  shows  that  on  the 
average  140,000  horse-power  are  continuously  radiated  from  every 
square  yard  of  the  sun's  surface.  In  order  to  generate  this  enor- 
mous energy  a  layer  of  anthracite  coal  25  feet  thick  would  have  to 
be  consumed  every  hour.  No  blast  furnace  so  far  devised  could 
develop  energy  at  this  enormous  rate.  Expressed  in  other  terms 
the  heat  of  the  sun  would  melt  a  layer  of  ice  4,000  feet  thick  every 
hour  over  its  whole  surface. 

It  is  a  certain  inference  from  the  great  rate  at.  which  the  sun 
radiates  heat  that  its  temperature  is  very  high.  It  is  not  easy  to 
measure  the  exact  temperature,  first,  because  it  is  higher  than  can 
be  produced  upon  the  earth,  and  second,  because  there  is  no  one  layer 
of  the  sun  which  alone  radiates  light  and  heat.  The  high  layers 
radiate  vast  quantities  and  in  turn  absorb  much  from  the  lower  lay- 
ers, which  are  also  radiating.  The  higher  layers  are  undoubtedly 
of  somewhat  lower  temperature  than  the  lower  layers.  But  all 
recent  determinations  agree  in  showing  that  the  temperature  of 
that  part  of  the  sun  which  radiates  light  and  heat  into  space  is  in 
the  neighborhood  of  10,000°  F.  This  is  several  thousand  degrees 
above  the  highest  temperature  so  far  obtained  in  the  most  powerful 
electrical  furnace,  and  is  sufficient  not  only  to  melt  but  also  to  vola- 
tilize all  substances  known  on  the  earth. 

Source  of  the  Sun's  Heat.  Since  the  sun  is  pouring  out  an 
enormous  quantity  of  energy  into  space,  it  would  cool  off  in  the 
course  of  time  unless  its  heat  were  in  some  way  replenished.  Of 
course,  since  it  is  a  very  large  body  it  would  not  cool  off  quickly. 
And  the  rate  at  which  a  body  cools  off  depends  not  only  on  its  size 
and  mass  but  also  upon  its  constitution.  For  example,  a  rock  of  a 


ASTRONOMY  201 

given  weight  will  cool  off  more  quickly  than  the  same  weight  of 
water;  or  expressed  otherwise,  it  takes  more  heat  to  raise  the  tempera- 
ture of  a  given  weight  of  water  than  it  does  to  raise  the  temperature 
of  the  same  weight  of  rock  to  an  equal  degree.  In  fact,  more  heat 
is  required  to  raise  the  temperature  of  a  given  mass  of  water  a  cer- 
tain'number  of  degrees  than  of  almost  any  other  known  substance. 
Now,  if  we  assume  that  the  sun  cools  off  as  slowly  as  water,  we  can 
compute  how  fast  its  temperature  will  fall  since  we  know  how  fast 
it  radiates  heat.  The  computation  shows  that  if  the  sun's  heat  were 
not  kept  up  by  some  process,  its  temperature  would  fall  about  four 
degrees  per  year.  Consequently  in  3,000  years  it  would  become  cold. 
This  proves  that  in  some  way  the  sun's  heat  is  continually  being 
restored. 

We  are  accustomed  to  associating  heat  with  fire,  and  it  seems 
perfectly  natural  to  imagine  that  the  sun  is  a  great  place  of  confla- 
gration, or. a  sort  of  furnace.  Now,  the  combustion  of  a  definite 
quantity  of  coal  produces  a  definite  quantity  of  heat,  and  it  is  easy 
to  see  that  one  can  calculate  how  long  the  heat  of  the  sun  would  be 
maintained  if  it  were  made  of  pure  coal  and  oxygen,  and  if  the  heat 
were  due  entirely  to  the  burning  of  the  coal.  It  is  found  on  making 
the  calculations  that,  according  to  this  theory,  the  heat  of  the  sun 
would  be  maintained  only  about  1,000  years.  The  theory  is  clearly 
inadequate  to  account  for  the  facts. 

About  1850  a  new  principle  in  physical  science,  known  as  the 
conservation  of  energy,  was  developed.  In  brief  it  is  that  the  total 
amount  of  energy  in  the  universe  does  not  change.  It  may  change 
its  form  but  not  its  quantity.  For  example,  if  a  body  is  in  motion 
it  has  a  certain  amount  of  energy  called  kinetic  energy.  If  it  strikes 
something  and  is  stopped  its  kinetic  energy  is  destroyed,  but  it  is 
found  that  in  place  of  the  kinetic  energy  its  temperature  has  been 
raised  by  the  impact.  Also  some  energy  has  been  given  forth  as 
sound.  But  neglecting  the  sound  and  all  the  energy  except  that 
which  is  manifested  in  the  increased  temperature  of  the  body,  it  is 
found  that  its  increase  in  temperature  is  exactly  equivalent  to  the 
kinetic  energy  it  had,  and  that  it  can  be  transformed  again  into 
kinetic  energy.  It  has  been  found  that  a  body  falling,  subject  to 
the  earth's  gravity,  772  feet  has  so  much  energy  of  motion  when  it 
strikes  that  its  temperature  is  raised  1°  C. 


202  ASTRONOMY 

Following  out  the  idea  of  falling  bodies,  it  was  suggested  about 
1850  that  the  sun's  heat  might  be  due  to  the  impact  of  meteors  fall- 
ing in  upon  it.  Because  of  the  great  gravitative  power  of  the  sun, 
a  meteor  would  strike  its  surface  with  a  velocity  of  about  480  miles 
per  second.  The  quantity  of  heat  generated  by  a  body  striking  the 
sun  at  such  an  enormous  velocity  would  be  thousands  of  times  that 
produced  by  the  combustion  of  any  mass  of  equal  weight.  But  when 
the  computations  were  made  to  determine  the  quantity  of  meteoric 
matter  which  would  be  required  to  keep  up  the  enormous  radiation 
of  the  sun,  it  was  found  that  it  was  so  great  that  in  its  passage  among 
the  planets  it  would  not  only  seriously  disturb  their  motions,  but 
would  sensibly  raise  the  temperatures  of  the  planets  themselves  by 
striking  in  upon  them.  If  this  meteoric  matter  came  from  space 
beyond  the  planets  it  would  produce  on  the  earth  about  sir  as  much 
energy  as  is  received  from  the  sun.  Since  this  is  millions  of  times 
as  much  energy  as  we  receive  from  the  meteors,  obviously  the  theory 
is  not  quantitatively  sound. 

Almost  at  the  time  of  the  development  of  the  meteoric  theory 
a  very  remarkable  contribution  was  made  to  the  subject  by  the  great 
German  physicist,  Helmholtz.  He  saw  that  if  the  sun  were  slowly 
contracting,  the  contraction  would  elevate  the  temperature  of  the 
sun  and  restore  its  heat.  A  contraction  of  a  body  is  equivalent  to 
a  small  fall  of  all  of  its  particles  towards  its  center.  While  at  first 
thought  one  might  suppose  this  would  be  quantitatively  insufficient, 
yet  the  computation  shows  that,  because  of  the  enormous  volume  of 
the  sun,  an  annual  contraction  of  about  180  feet  in  the  sun's  radius 
would  account  for  all  the  heat  and  light  it  radiates.  So  small  a  con- 
traction on  so  large  and  distant  an  object  as  the  sun  would  not  become 
visible  with  even  our  best  instruments  until  it  had  continued  more 
than  6,000  years.  In  1870,  Lane  showed  that  a  gaseous  body  radiat- 
ing heat  into  space  would  necessarily  contract,  and  that  in  contract- 
ing its  heat  would  not  only  be  restored  but  its  temperature  would 
actually  rise  so  long  as  it  remained  gaseous. 

According  to  the  contraction  theory,  which  is  quantitatively  very 
much  more  satisfactory  than  any  earlier  one,  the  sun  was  larger  in 
the  past  than  it  is  at  present,  and  in  the  future  it  will  become 
continually  smaller.  This  enables  us  to  compute  how  long  the  sun 
can  have  radiated  light  and  heat  sensibly  at  its  present  rate.  In 


ASTRONOMY  203 

making  the  computation  for  its  effects  on  the  earth,  we  do  not  need 
to  follow  it  back  beyond  the  time  when  it  extended  out  to  the  earth. 
The  computation  shows  that  if  the  contraction  theory  is  correct,  and 
if  the  shrinking  of  the  sun  is  the  only  source  of  its  energy,  then  it 
can  not  have  radiated  light  and  heat  on  the  earth  at  its  present  rate 
more  than  about  20,000,000  years.  If  this  is  the  whole  story,  the 
series  of  changes  through  which  the  earth  has  passed  and  the  evolu- 
tion of  plants  and  animals  which  live  upon  it  have  taken  place 
inside  of  20,000,000  years.  Turning  to  the  future,  we  can  calculate 
how  long  it  will  be  before  the  density  of  the  sun  will  become  so 
great  that  further  contraction  will  be  impossible.  Assuming  that  it 
will  not  contract  further  when  it  gets  as  dense  as  iron,  it  follows 
that  the  future  existence  of  the  sun  as  an  efficient  source  of  light  and 
heat  will  extend  over  only  8,000,000  or  10,000,000  years. 

The  contraction  theory  of  the  heat  of  the  sun  certainly  is  sound, 
and  until  recently  was  supposed  to  be  the  only  source  of  the  sun's 
energy.  On  the  basis  of  the  computations  just  mentioned,  physicists 
and  astronomers  made  rather  definite  statements  of  the  age  of  the 
earth  and  the  period  during  which  evolution  on  its  surface  could 
have  taken  place.  The  geologists  and  the  zoologists  on  the  basis  of 
data  in  their  own  sciences  came  to  the  conclusion  that  the  earth 
has  been  undergoing  an  evolution  much  longer  than  20,000,000  years. 
They  were  by  no  means  in  harmony  on  the  matter,  for  their  esti- 
mates ranged  all  the  way  from  50,000,000  to  500,000,000  years. 
Recently  we  have  found  reasons  for  believing  that  perhaps  there  are 
other  important  sources  of  heat  in  the  sun.  Since  the  discovery  of 
X-rays  and  radium  it  has  been  found  that  certain  kinds  of  matter 
undergo  disintegration.  That  is,  certain  large  molecules  such  as 
those  of  radium  and  uranium  break  up  into  molecules  of  smaller 
weight,  and  in  the  process  of  disintegration  give  forth  enormous 
quantities  of  energy.  The  amount  of  energy  is  of  the  order  of  1,000,- 
000  times  that  produced  in  the  combustion  of  equal  weights  of  any 
known  substance.  One  of  the  products  of  disintegration  of  radium 
is  helium.  Now  radium  is  not  certainly  known  to  exist  in  the  sun, 
but  helium  is  extremely  abundant  there.  In  fact,  helium  was  first 
known  in  the  sun,  and  its  name  comes  from  the  Greek  word  for  sun. 
The  fact  that  helium  is  abundant  in  the  sun,  perhaps  can  be  inter- 
preted as  indicating  that  radium  is  there  and  has  been  undergoing 


204  ASTRONOMY 

disintegration.  It  is  certainly  possible,  therefore,  and  indeed  probable, 
that  an  important  source  of  the  sun's  energy  is  the  disintegration  of 
matter.  It  is  well  within  the  bounds  of  possibility  that  this  is  the 
most  important  source  of  its  energy.  At  the  present  time  there  is 
no  reason  to  conclude  that  the  sun  has  radiated  light  and  heat  at 
its  present  rate  for  only  20,000,000  years.  The  period  may  just  as 
well  be  10  or  50  times  as  long.  Similarly,  there  is  now  no  reason  to 
suppose  that  in  8,000,000  or  10,000,000  years  in  the  future  its  light 
will  begin  to  fail.  While  no  positive  statements  can  be  made  regard- 
ing the  matter,  it  does  not  seem,  in  the  light  of  our  present  knowl- 
edge, unreasonable  to  suppose  that  the  future  existence  of  the  sun  and 
earth  in  approximately  their  present  states  will  extend  over  many 
hundreds  of  millions  of  years. 

Sun  Spots.  The  most  conspicuous  markings  ever  observed  upon 
.the  sun  are  relatively  dark  spots  which  frequently  appear  in  its 
luminous  surface  and  last  from  a  few  days  to  a  few  months.  The 
opaque,  extremely  luminous  surface  of  the  sun  is  called  the  photo- 
sphere. The  sun  spots  are  phenomena  of  the  atmosphere.  They  are 
composed  of  a  dark  nucleus,  called  the  umbra,  which  is  surrounded 
by  a  somewhat  lighter  band,  called  the  penumbra.  The  penumbra 
often  is  composed  of  a  series  of  filaments  reaching  from  the  light 
photosphere  into  the  umbra.  The  spots  have  been  spoken  of  as 
being  dark.  This  statement  is  slightly  misleading,  for  they  are  only 
relatively  dark  with  respect  to  the  intensely  luminous  photosphere. 
The  actual  umbrae  of  the  spots  are  as  bright  as  the  most  intense 
artificial  light  we  have. 

The  diameters  of  the  spots  may  be  anywhere  from  500  to  50,000 
miles,  and  some  penumbrae  reach  up  to  200,000  miles.  Often  a 
single  penumbra  may  contain  many  umbrae  in  its  interior.  The 
development  of  a  sun  spot  is  usually  preceded  by  indications  of 
violent  disturbance  in  its  region,  and  bright  points  with  intervening 
dark  places  are  generally  observed  immediately  before  the  appear- 
ance of  a  spot.  The  dark  places  unite  and  form  a  spot  after  an 
interval  of  a  few  hours  or  in  some  cases  a  few  days. 

The  sun  spots  have  the  appearance  of  being  dark  holes  in  the 
surface  of  the  sun.  We  unconsciously  draw  this  conclusion  because 
our  experience  on  the  earth  tells  us  that  holes  into  its  interior,  such 
as  tunnels  and  the  mouths  of  mines,  appear  dark.  If  our  experience 


ASTRONOMY 


205 


had  been  the  opposite,  then  undoubtedly  a  dark  spot  on  a  distant 
world  would  appear  as  a  mountain  to  us  instead  of  a  hole  into  its 
interior.  Such  a  conclusion  would  be  more  nearly  correct  in  the 
case  of  the  sun  spots.  Instead  of  being  dark  openings  into  the 
interior  of  the  sun  they  are  masses  of  cooler  gas  which  are'  usually 


Fig.  92.     Photograph  of  the  Sun  Showing  Spots  on  Its  Surface 

above  the  general  surface  of  the  sun's  photosphere.  (See  Fig.  92.) 
This  is  proved  by  the  fact  that  as  they  appear  near  the  margin  of 
the  sun  they  are  relatively  more  conspicuous  than  they  are  at  the 
center  of  its  disk.  Fig.  92  is  a  direct  photograph  of  the  whole  disk 
of  the  sun  showing  several  spots  and  the  absorption  near  its  margin. 
The  number  of  sun  spots  varies  greatly  from  year  to  year  and 
they  are  not  uniformly  distributed  on  the  sun.  They  occur  in  greater 


206  ASTRONOMY 

numbers  for  a  few  years  and  then  are  less  numerous,  running  through 
the  cycle  of  changes  in  about  11  years.  They  appear  in  greatest 
numbers  in  belts  on  each  side  of  the  sun's  equator.  When  they 
begin  to  become  more  numerous,  they  appear  first  in  greatest  num- 
bers at  latitudes  about  35  degrees  north  and  south  of  the  equator. 
As  time  goes  on  they  appear  most  frequently  in  lower  and  lower 
latitudes,  reaching  their  greatest  numbers  when  they  are  at  about 
20  degrees  north  and  south  of  the  equator.  Then  they  begin  to 
diminish  in  number  and  size  and  disappear  at  latitudes  approxi- 
mately 6  degrees  north  and  south.  At  the  same  time  a  new  series 
begins  in  the  higher  latitudes. 

From  the  observations  of  sun  spots  it  has  been  possible  to 
determine  the  rate  of  rotation  of  the  sun.  Considered  as  a  whole, 
its  period  of  rotation  is  about  26  days,  and  its  motion  is  in  the 
same  direction  as  that  of  the  revolution  of  the  planets  around  it. 
The  sun  does  not  rotate  as  a  solid,  but  its  equatorial  zone  moves 
faster  than  those  parts  in  higher  latitudes.  The  equator  rotates  in 
a  period  of  about  25  days,  spots  in  latitude  30  degrees  complete  their 
revolution  in  about  26J  days,  and  those  in  latitude  45  degrees  in 
about  27  days.  Spots  are  not  seen  in  latitudes  higher  than  45 
degrees.  The  rotation  of  the  sun  has  been  determined  in  several 
other  ways,  principally  by  observations  of  bright  spots  and  great 
elevations  which  the  spectroscope  shows,  and  there  is  in  a  general 
way  agreement  of  these  results  with  those  obtained  by  the  obser- 
vations of  spots. 

Different  Layers  of  the  Sun.  The  lowest  layer  in  the  sun 
which  we  can  see  is  the  photosphere,  mentioned  above.  It  is  the 
opaque,  apparently  solid  or  liquid  surface  of  the  sun.  Certainly, 
instead  of  being  in  a  solid  or  liquid  state,  it  is  almost  entirely  gaseous 
because  of  the  sun's  high  temperature.  It  is  largely  composed  of  the 
ordinary  terrestrial  elements  in  a  gaseous  state,  and  has  the  appear- 
ance of  being  a  continuous  surface  because  of  the  immense  numbers 
of  small  liquid  particles  of  carbon,  rock  material,  and  iron  floating 
in  it.  It  is  somewhat  analogous  to  clouds  in  our  atmosphere.  A 
cloud  appears  to  be  an  opaque  solid  substance  when  seen  at  a  dis- 
tance, but  as  a  matter  of  fact  it  is  almost  entirely  gaseous.  It  gets 
its  appearance  from  great  numbers  of  minute  particles  of  water 
floating  in  the  atmosphere. 


Fig.  93.     The  Sun's  Photosphere  Highly  Magnified 


208 


ASTRONOMY 


In  Fig.  93  is  shown  a  small  portion  of  the  photosphere  highly 
magnified.  It  is  seen  to  be  composed  of  a  large  number  of  minute 
granules  with  darker  places  between.  The  light  spots  are  the  tops 
of  ascending  currents  which  are  bringing  the  heated  material  up 
from  the  interior  to  restore  that  lost  by  radiation;  the  darker  places 


Fig.  94.       Eruptions  from  the  Sun  Photographed  at  the  Yerkes  Observatory  by  Fox 

are  where  the  partially  cooled  gases  are  sinking  back  into  the  depths. 
These  bright  spots  are  generally  from  500  to  1,000  miles  in  diameter. 
Above  the  photosphere  lies  a  less  intensely  heated  atmosphere, 
called  the  reversing  layer,  which  contains  at  least  about  half  of  our 
terrestrial  elements,  all  in  the  gaseous  state.  Among  these  elements 
are  a  large  fraction  of  the  metals  with  which  we  are  familiar.  The 
thickness  of  the  reversing  layer  averages  about  500  or  600  miles. 


ASTRONOMY  209 

Mixed  throughout  it  and  possibly  to  some  extent  below  it,  is  a  thin 
cloud  of  small  liquid  or  solid  particles.  The  effect  of  this  cloud  is  to 
absorb  some  of  the  light  radiated  by  the  photosphere  and  to  reduce 
its  intensity,  particularly  near  the  margin,  as  is  shown  in  Fig.  92. 
Above  the  reversing  layer  is  what  is  called  the  chromosphere  (color 
sphere).  This  is  a  gaseous  envelope  of  5,000  to  10,000  miles  in 


Fig.  95.     The  Sun's  Corona  Photographed  at  the  Time  of  a  Total  Eclipse  of  the  Sun 
in  1900 

depth.  At  the  time  of  total  eclipse  it  can  be  seen  as  a  scarlet  ring 
surrounding  the  entire  sun,  whose  surface  seems  to  be  seething  with 
tongues  of  leaping  flames.  The  spectroscope  shows  that  the  chromo- 
sphere is  made  up  of  luminous  hydrogen,  helium,  and  calcium. 

The  photosphere  seems  to  be  relatively  quiet  and  continuous 
except  where  it  is  broken  up  by  the  spots.    On  the  other  hand,  the 


210  ASTRONOMY 

chromosphere  is  the  seat  of  numerous  disturbances.  Vast  eruptions, 
called  prominences,  rise  up  from  it  to  altitudes  of  from  50,000  to 
300,000  miles  with  velocities  sometimes  as  great  as  500  miles  per 
second.  Fig.  94  is  a  photograph  of  some  of  these  remarkable  streams 
of  material.  On  the  sun  explosions  frequently  take  place  in  which 
masses  of  matter,  whose  volumes  are  greater  than  that  of  the  earth, 
are  thrown  aloft  to  a  distance  farther  than  from  the  earth  to  the 
moon.  This  material,  which  rises  in  prominences,  goes  up  and  often 
turns  over  in  long  graceful  streamers  similar  to  the  path  of  a  sky- 
rocket, and  plunges  back  again  upon  the  sun. 

Outside  of  the  chromosphere  is  the  corona,  a  vast  envelope 
surrounding  the  sun  and  reaching  out  to  500,000  or  1,000,000  miles 
from  it.  The  corona  can  be  observed  only  at  the  time  of  total  eclipse 
because  it  is  so  faint  that  the  illumination  of  our  atmosphere  entirely 
obscures  it.  It  has  some  of  the  properties  of  an  atmosphere,  and 
some  which  are  considerably  different.  It  does  not  uniformly  sur- 
round the  sun  but  stretches  out  farthest  in  the  plane  of  its  equator. 
Its  shape  varies  from  time  to  time  with  the  period  of  the  sun  spot 
activities,  and  is  undoubtedly  associated  with  the  disturbances  on 
the  sun's  surface.  Around  the  poles  of  the  sun  it  is  arranged  in 
streaks,  showing  that  strong  magnetic  forces  are  at  play  there. 

Fig.  95  shows  a  photograph  of  the  corona  at  the  time  of  a  total 
eclipse  in  1900. 

Spectrum  Analysis.  When  substances  are  in  the  gaseous  state 
and  luminous,  they  give  forth  vibrations  whose  character  depends 
upon  their  chemical  constitution.  The  vibrations  are  distinguished 
from  one  another  chiefly  by  their  frequency,  or  the  number  given 
out  per  second.  For  example,  incandescent  hydrogen  gives  vibrations 
of  a  certain  frequency,  and  incandescent  oxygen  gives  vibrations  of 
quite  a  different  frequency,  and  so  on  for  all  the  elements.  The 
different  light  radiations  from  different  elements  are  somewhat 
analogous  to  the  different  sound  vibrations  given  forth  by  different 
kinds  of  bells,  the  pitch  depending  upon  the  number  of  sound  waves 
given  out  per  second.  The  reason  that  the  matter  must  be  in  the 
gaseous  state  in  order  to  get  its  characteristic  spectrum,  is  that 
when  it  is  in  the  solid  or  liquid  state,  the  vibrations  of  the  parts  of 
the  molecules  which ,  produce  the  light  waves  are  interfered  with  by 
their  being  restrained  by  the  neighboring  molecules,  and  are  there- 


ASTRONOMY 


211 


fore,  not  free  to  vibrate  with  their  normal  frequency.  But  when 
matter  is  in  the  gaseous  state,  as  was  explained  in  connection  with 
the  atmosphere,  the  molecules  are  independent  of  one  another,  ex- 
cept for  brief  times  during  collisions,  and  the  normal  oscillations 
take  place  unhampered.  Consequently,  the  character  of  the  vibra- 
tions of  the  molecules  depends  simply  upon  their  structure.  It  is 
clear  from  this  that  if  some  means  can  be  devised  of  discovering  the 
character  of  the  vibrations  coming  from  a  luminous  gas,  its  nature 
can  be  determined  in  this  fashion.  The  spectroscope  is  an  instru- 
ment precisely  for  this  purpose. 

Fig.  96    shows    the   principles  upon  which  spectrum  analysis 
depends,  though  an  instrument  for  practical  use  is  modified  so  as 


Fig.  96.     Diagram  Showing  the  Dispersion  of  Light  Which  Passes  Through  a  Prism. 
Dispersion  is  at  the  Basis  of  Spectrum  Analysis 

to  get  a  brighter  spectrum.  Let  L  be  a  dense  beam  of  parallel  rays 
of  white  light  which  fall  on  the  screen  S,  at  0.  Suppose  0  is  a  narrow 
opening  of  the  slit  through  Si,  which  may  be  from  T^TT  to-nnnr  of  an 
inch  wide.  A  thin  slice  of  light  passes  through  0  and  falls  on  the 
prism  P.  It  strikes  the  first  surface  of  P  obliquely  and  its  direction 
is  bent  as  it  enters  it.  The  direction  of  the  light  is  not  only  bent, 
but  the  light  is  spread  out  into  its  different  colors.  When  the  light 
emerges  from  P  it  is  bent  still  farther  and  spread  out  still  more.  It 
may  be  caught  upon  the  screen  S2,  when  it  will  be  found  that  it 
consists  of  a  band  of  colors  varying  from  the  violet  v  on  the  end 
which  is  bent  the  more,  to  the  red  r  on  the  other  end.  The  violet 
rays  are  the  shortest  (that  is,  the  rays  with  Ihe  greatest  frequency) 
are  visible  to  the  human  eye,  and  the  red  are  the  longest. 


212  ASTRONOMY 

Beyond  the  violet  there  are  the  chemical  rays  and  beyond  the  red 
in  the  other  direction  the  heat  rays. 

Now,  suppose  a  single  substance  in  the  gaseous  state  is  heated 
to  incandescence.  For  example,  let  us  consider  sodium,  which  is  the 
metal  constituent  of  ordinary  salt.  The  light  will  appear  to  the  eye 
as  yellow  and  when  it  passes  through  the  prism  and  falls  on  the 
screen  S2,  there  will  be  seen  light  at  two  places  near  together  in  the 
yellow.  That  is,  sodium  in  the  incandescent  gaseous  state  gives  forth 
vibrations  of  two  different  frequencies  which  are  so  near  together 
that  they  both  are  yellow  light.  It  is  found  by  experiment  in  the 
laboratory  that  sodium  always  gives  these  two  kinds  of  yellow  light, 
and  that  no  other  substance  gives  exactly  the  same  kinds  of  light. 
It  must  be  understood  that  the  actual  instruments  in  use  are  much 
more  powerful  and  give  a  much  brighter  spectrum  than  that  indi- 
cated in  the  simple  sketch  of  Fig.  96.  Now,  suppose  iron  is  made 
incandescent  and  that  it  is  in  the  gaseous  state.  When  its  light  is 
passed  through  the  prism  P  and  falls  on  the  screen  S2,  it  will  be 
found  that  there  are  bright  lines  at  very  many  places.  The  iron 
molecule  seems  ;to  be  extremely  complex  and  gives  forth  many  kinds 
of  vibrations,  but  the  important  fact  in  this  connection  is  that  it 
always  gives  the  same  vibrations  and  it  gives  no  vibrations  which 
are  emitted  by  any  other  substance  whatever. 

Now,  suppose  that  the  light  instead  of  coming  from  a  point  in 
the  laboratory  comes  from  the  distant  sun,  or  even  from  the  much 
more  distant  stars.  The  character  of  its  vibrations  will  not  have 
been  changed  in  its  journey  through  space  any  more  than  the  char- 
acter of  the  vibrations  from  a  musical  instrument  will  be  changed  by 
passing  some  distance  through  the  air;  the  tune  is  the  same  whether 
the  instrument  is  near  to  us  or  far  from  us.  It  follows  that  if  the 
distant  object  is  an  incandescent  gas  its  light  will  be  analyzed  into 
its  separate  parts  and  will  fall  on  the  screen  S2  at  distant  places, 
depending  upon  the  constitution  of  the  gas.  If  the  substance  is  one 
with  which  we  have  become  familiar  in  our  laboratories  we  shall 
recognize  its  presence  by  the  character  of  its  light  when  analyzed. 
In  fact,  if  the  source  of  light  is  composed  of  a  mixture  of  many 
substances  the  presence  of  all  of  them  can  be  determined,  for  though 
originally  it  is  a  mixture  of  various  colors  the  spectroscope  will  sepa- 
rate them  into  their  constituent  parts  and  each  one  will  be  distinct 


ASTRONOMY  213 

from  every  other.  For  example,  if  there  were  a  mixture  of  sodium 
and  iron  the  yellow  lines  of  sodium  would  appear  in  the  spectrum, 
and  also  the  numerous  lines  of  the  iron.  When  the  light  is  thus 
analyzed  into  its  separate  parts,  the  presence  of  one  kind  of  lines 
does  not  interfere  with  the  detection  of  any  other  kind.  It  is  clear, 
therefore,  from  all  of  this  discussion  that  the  chemical  constitution 
of  an  incandescent  gas  can  be  determined  by  means  of  the  spectro- 
scope, however  far  away  it  is  in  space.  This  remarkable  process  has 
been  understood  for  about  50  years.  Before  its  discovery  it  was 
supposed  that  while  we  can  determine  the  motions  of  the  heavenly 
bodies  and  in  most  cases  their  masses  and  dimensions,  nevertheless, 
their  constitution  was  a  field  forever  closed  to  us. 

There  is  another  phase  to  spectrum  analysis  which  in  application 
is  often  more  important  than  the  preceding  results.  Suppose  the 
light  L  is  white;  that  is,  that  it  comes  from  an  incandescent  solid 
or  liquid.  Then,  as  has  just  been  explained,  its  spectrum  will  be 
continuous,  and  the  substance  of  which  it  is  composed  can  not  be 
determined.  But  suppose  that  between  Sl  and  P  there  is  interposed 
a  cooler  gas.  This  does  not  mean  by  any  means  that  it  shall  be  cold, 
but  simply  that  it  shall  be  less  luminous  than  the  source  of  the 
light  L.  This  cooler  gas  will  absorb  some  of  the  light  L,  and  the 
important  fact  is  that  it  absorbs  precisely  those  vibrations  which  it 
would  itself  give  out  if  it  were  incandescent.  For  example,  suppose 
the  cooler  gas  between  Si  and  P  is  sodium.  Then  the  spectrum  on 
£2,  instead  of  being  a  continuous  band  of  light  from  the  violet  to 
the  red,  will  be  a  continuous  band,  except  where  it  is  crossed  by 
two  dark  lines  in  the  yellow  at  precisely  the  place  where  the  yellow 
bands  of  sodium  fall.  That  is,  the  interposed  sodium  gas  has  been 
transparent  to  all  the  colors  except  those  which  it  itself  radiates. 
This  absorption  by  a  gas  of  the  same  colors  it  radiates  is  analogous 
to  the  fact  that  a  musical  instrument,  for  example  a  piano,  will  take 
up  those  same  vibrations  when  produced  on  another  instrument  that 
it  is  capable  of  giving  forth.  If  middle  C  on  one  piano  is  struck  and 
the  key  of  middle  C  held  down  on  a  neighboring  one,  the  second  one 
will  be  set  vibrating  by  the  first,  but  if  D  be  held  down  on  the  second 
one  no  sensible  vibrations  will  be  induced. 

It  follows  from  these  principles  that  if  the  source  of  light  is  an 
incandescent  solid,  and  if  a  cooler  gas  is  between  it  and  the  observer, 


214 


ASTRONOMY 


I 


Fig.  97.     A  Portion  of  the 

Solar  Spectrum  on  a 

Large  Scale 


he  can  determine  the  chemical  constitution  of 
the  interposed  cooler  gas  but  not  of  the  actual 
source  of  light.  Let  us  apply  these  results  to 
the  sun.  The  photosphere  is  the  main  source 
of  light  in  it  and,  as  has  been  explained,  the 
photosphere  owes  ^ts  intense  luminosity  and 
opaque  appearance  to  the  fact  that  it  is  made 
up  of  small  drops  of  liquid  particles  of  carbon, 
iron,  rock  material,  etc.  The  light  from  this 
photosphere  passes  through  the  cooler  gaseous 
envelope  above  it,  called  the  reversing  layer. 
The  reversing  layer  subtracts  from  the  light  of 
the  photosphere  certain  rays  and  produces 
many  dark  lines  in  the  sun's  spectrum,  which 
would  otherwise  be  continuous.  Fig.  97  shows 
a  small  part  of  the  solar  spectrum;  the  left 
part  is  the  spectrum  of  the  photosphere  and 
the  right  that  of  a  spot.  With  the  powerful 
modern  instruments  20,000  lines  can  be 
observed  in  the  spectrum  of  the  sun.  So  far 
about  12,000  of  these  lines  have  been  meas- 
ured. While  not  all  of  them  have  been  iden- 
tified with  terrestrial  substances,  about  half  of 
the  elements  known  to  the  earth  have  been 
found  to  exist  in  the  sun.  Among  the  more 
common  ones  we  may  mention  hydrogen, 
helium,  carbon,  oxygen,  sodium,  magnesium, 
aluminum,  silicon,  potassium,  calcium,  iron, 
nickel,  copper,  zinc,  silver,  tin,  and  lead.  The 
state  of  the  sun  can  be  imagined  when  it  is 
found  that  in  its  cooler  atmosphere  all  of  these 
elements  are  in  a  gaseous  condition. 

Another  very  interesting  application  of  the 
spectroscope  has  been  made  in  the  photography 
of  the  sun.  In  the  case  of  certain  lines,  the 
vapors  which  surround  the  photosphere  are 
so  extensive  and  so  dense  that  they  cut  out 
nearly  all  the  light  which  comes  from  it,  but 


ASTRONOMY 


215 


above  these  vapors  there  are  floating  luminous  clouds  of  the 
same  material.  The  width  of  an  absorption  line  increases  with  the 
density  of  the  absorbing  medium.  In  the  case  under  consideration 
the  lines  are  wide  because  of  the  density  of  the  absorbing  gases  which 
are  subject  to  great  pressure.  The  higher  luminous  gases  are  subject 
to  less  pressure  and  give,  therefore,  a  bright  line  in  the  center  of 
the  dark  absorption  line.  That  is,  in  the  sun's  spectrum  in  the  case 
of  some  wide  heavy  lines  there  are  bright  centers.  The  light  in 
these  centers  comes  from  definite  elements.  When  the  sun's  light  is 


Fig.   98.     Photographs  of  Spots  Taken  with  Calcium  Light 

spread  out  into  a  spectrum  so  that  the  light  from  each  incandescent 
substance  comes  out  in  a  different  place,  it  may  all  be  screened  off 
except  that  which  comes  from  a  single  substance,  If  a  photograph 
is  taken,  a  picture  of  the  sun  is  obtained  with  the  light  which  comes 
from  a  single  element.  In  order  to  obtain  a  photograph  of  the  whole 
sun  it  is  necessary  to  have  the  apparatus  adjusted  so  that  the 
photographic  plate  will  move  at  the  same  time  the  spectroscope  is 
pointed  at  different  parts  of  the  sun,  for  otherwise  the  images  of 
different  parts  would  fall  upon  the  same  part  of  the  photographic 
plate,  and  we  should  obtain  a  composite  picture  rather  than  a  picture 


216  ASTRONOMY 

of  its  whole  surface.  When  the  instrument  is  properly  adjusted,  a 
photograph  of  the  whole  sun  in  light  from  one  element  is  obtained, 
and  the  picture  shows  distribution  of  this  element  in  the  sun  at  the 
time  in  question.  This  instrument  is  called  the  spectroheliograph. 

Figs.  98  and  99  are  spectroheliograms  of  the  sun.  Fig.  98 
shows  a  small  portion  of  the  solar  disk  including  some  spots  as 
photographed  with  calcium  light,  and  Fig.  99  shows  the  same  region 
as  photographed  with  hydrogen  light.  The  luminous  places  are 
where  the  element  in  question  was  abundant  in  an  incandescent 


Fig.  99.    Photograph  of  the  Same  Spots  as  Shown  in  Fig.  98  Taken  with  Hydrogen  Light 

state.  The  relatively  dark  places  are  where  the  element  was  present, 
but  in  such  a  cool  condition  that  it  absorbed  almost  completely  the 
light  from  the  photosphere. 

THE  SIDEREAL  SYSTEM 

Distribution  of  Stars.  In  connection  with  the  work  on  constel- 
lations we  saw  that  stars  were  apparently  grouped  in  various  parts 
of  the  sky.  This  apparent  aggregation  here  and  there  depends,  of 
course,  upon  our  position  with  respect  to  them.  At  present  we  are 
not  interested  in  their  apparent  grouping,  but  in  their  actual  distri- 
bution in  space.  This  is,  of  course,  related  somewhat  to  their  apparent 


ASTRONOMY  217 

distribution;  or,  at  least,  their  apparent  distribution  depends  partly 
upon  their  actual  distribution. 

An  examination,  either  without  a  telescope  or  with  a  telescope, 
shows  that  the  stars  are  much  more  numerous  in  the  direction  of 
the  Milky  Way  than  they  are  in  directions  at  right  angles  to  it.  If 
a  given  area  be  counted  in  the  plane  of  the  Milky  Way  and  an  equal 
area  be  counted  at  right  angles  from  it,  it  will  be  found,  especially 
if  very  faint  stars  are  included,  that  the  region  in  the  Milky  Way 
has  many  times  more  stars  than  the  other  one.  It  follows  that  stars 
are  either  more  closely  crowded  together  in  the  direction  of  the 
Milky  Way,  or  that  in  those  directions  we-  are  looking  through  a 
greater  depth  of  them.  That  is,  appearances  have  led  to  the  conclu- 
sion that  the  system  of  the  stars  is  a  great  disk  or  grindstone-shaped 
figure  in  space.  The  sun  and  its  family  of  planets  is  somewhere  in 
the  interior  of  this  vast  aggregation  of  stars.  The  plane  of  the  disk 
is  the  plane  of  the  Milky  Way.  When  we  look  out  in  the  direction  of 
the  Milky  Way  we  see  a  vast  aggregation  of  stars  because  we  are 
looking  through  a  greater  depth  of  them;  and  when  we  look  out  at 
right  angles  to  it  we  see  fewer  stars  because  we  are  looking  in  a 
direction  where  we  sooner  reach  the  borders  of  the  system. 

The  fact  that  photographs  of  the  Milky  Way  show  dark  rifts 
and  breaks,  as  in  Fig.  37,  is  against  this  theory  without  some  con- 
siderable modifications.  Recent  studies  of  the  apparent  motions 
of  the  stars  show  that  those  so  far  examined,  which,  of  course,  do 
not  include  the  great  majority  of  those  stars  which  are  extremely 
faint,  belong,  on  the  whole,  to  two  great  star  streams.  Probably 
the  sidereal  system  is  made  up  of  a  relatively  small  number  of  great 
star  families,  the  numbers  of  which  move  in  parallel  lines  with 
approximately  the  same  speed. 

Most  of  the  stars  are  so  remote  from  us  that  their  distances 
can  not  be  found  by  direct  processes.  One  of  the  proofs  of  the  earth's 
revolution  around  the  sun  is  the  parallax  that  certain  stars  are 
observed  to  have.  (See  Fig.  20.)  But  parallaxes  of  a  sufficient  num- 
ber of  stars  can  not  be  obtained  by  this  method  to  give  any  general 
idea  of  their  distances  when  considered  as  a  whole.  There  are,  how- 
ever, certain  indirect  processes  which  have  led  to  most  interesting 
results.  If  the  stars  were  still  and  the  sun  in  motion,  they  would 
apparently  drift  back  in  the  direction  opposite  to  that  of  the  motion 


218  ASTRONOMY 

of  the  sun.  The  apparent  rate  at  which  they  would  drift  back  would 
depend  upon  their  distance  from  the  sun.  It  is  analogous  to  what 
one  observes  when  he  passes  through  the  country  on  a  train;  the 
objects  which  are  near  apparently  go  back  at  a  high  speed,  while 
those  which  are  far  away  seem  to  move  very  slowly.  Now,  in  the 
case  of  the  stars,  if  the  rate  at  which  they  apparently  go  back  were 
observed,  their  distances  could  be  computed.  If  their  motions  in 
the  backward  direction  were  not  enough  so  they  could  be  observed 
in  one  year,  then  perhaps  they  could  be  observed  in  10  years,  or  100 
years.  In  this  way  the  distances  of  all  the  stars  which  are  not  in 
the  direction  in  which  the  sun  is  going,  or  in  that  from  which  it  has 
come,  could  be  determined. 

Unfortunately  for  the  application  of  this  method  the  stars  are 
not  at  rest.  The  spectroscope  and  a  study  of  their  apparent  motions 
show  that  on  the  whole  they  are  moving  at  the  rate  of  several  hundred 
millions  of  miles  per  year.  It  follows  that  the  distance  of  any  one 
star  can  not  be  determined  from  its  apparent  backward  drift  because 
this  depends  not  only  upon  the  motion  of  the  sun  but  also  upon  its 
own  motion.  But  taking  the  stars  as  a  whole  their  distances  can  be 
determined  in  this  fashion.  On  the  whole,  they  will  not  be  moving 
in  one  direction  more  than  another,  and  it  is  possible,  therefore,  by 
an  averaging  process  for  any  group  of  stars,  say  of  a  definite  mag- 
nitude, to  find  their  average  distance  from  the  sun. 

The  stars  belong  to  two  main  types,  depending  upon  the  kind 
of  light  they  send  to  us  as  determined  by  the  spectroscope.  The 
stars  of  Type  I  are  those  which  are  blue,  or  bluish  white,  and  are 
supposed  to  be  in  an  early  stage  of  their  evolution.  The  stars  of 
Type  II  are  yellow  and  similar  to  the  sun.  It  is  found  that  the  stars 
of  Type  I  of  a  given  magnitude  are  on  the  average  considerably 
farther  from  us  than  those  of  Type  II. 

A  statistical  study  shows  that  on  the  average  first  magni- 
tude stars  of  Type  I  are  so  far  away  that  it  takes  their  light  about 
one  hundred  years  to  come  to  the  earth,  while  light  from  first  mag- 
nitude stars  of  Type  II  comes  to  us  in  about  43  years.  The  formulas 
on  which  the  computations  are  made  are  based  upon  stars  of  the  first 
nine  or  ten  magnitudes.  They  are  probably  not  very  exact  for  the 
brighter  stars,  because  there  are  too  few  of  them  to  make  the  statis- 
tical method  very  safe;  and  they  are  probably  inexact  for  the  very 


ASTRONOMY  219 

faint  stars,  because  they  have  not  been  used  in  deriving  the  formulas. 
But  applying  the  formulas  it  is  found  that  on  the  average  the  light 
of  the  ninth  magnitude  stars  of  Type  I  is  more  than  700  years  com- 
ing to  us,  and  of  Type  II  a  little  more  than  300  years.  From  the 
same  formulas  it  is  found  that  the  light  of  stars  of  the  fifteenth  mag- 
nitude of  Type  I  reaches  us  more  than  3,000  years  after  it  leaves  the 
stars  which  radiated  it,  and  of  Type  II,  more  than  1400  years. 

In  getting  these  results  it  has  been  necessary  not  only  to  observe 
the  apparent  motions  of  the  stars  but  to  know  the  rate  at  which  the 
sun  is  moving  relatively  to  them.  The  motion  of  the  sun  is  deter- 
mined by  means  of  the  spectroscope.  The  velocities  of  many  stars 
relative  to  the  sun  are  found,  and  by  an  averaging  process  it  can  be 
determined  from  these  data  in  what  direction  the  sun  moves  and 
with  what  speed.  Thus  we  have  the  remarkable  result  that  the 
spectroscope,  which  can  not  be  used  in  measuring  distances  directly, 
is  indirectly  used  in  determining  the  distances  of  stars  so  remote 
that  the  ordinary  means  entirely  fail.  It  is  characteristic  of  science 
that  various  methods  are  woven  together  to  secure  its  results. 

In  order  to  determine  the  magnitude  of  the  sun  relatively  to 
other  stars  we  can  compute  how  bright  it  would  be  if  it  were  at  the 
distance  of  the  average  first-magnitude  stars  of  either  Type  I  or 
Type  II.  The  direct  measurements  of  the  light  received  from  the 
sun  show  that  its  magnitude  is  about  —26.4,  and  it  follows  that  if 
it  were  at  the  average  distance  of  the  first-magnitude  stars  of  Type 
I  it  would  be  only  a  little  brighter  than  an  eighth-magnitude  star, 
or  ?iff  as  bright  as  an  average  star  of  Type  I.  If  it  were  at  the  average 
distance  of  the  first-magnitude  stars  of  Type  II  it  would  be  of  the 
sixth'  magnitude,  or  about  riir  as  bright  as  the  average  star  of  Type 
II.  It  is  thus  apparent  that  our  sun  is  considerably  below  the  average 
of  other  suns  in  magnitude. 

Groups  of  Stars.  The  results  given  in  the  preceding  section 
refer  to  stars  as  a  whole  and  do  not  take  into  account  their  groupings. 
Just  as  the  sky  is  seen  to  contain  groups  of  stars,  so  the  measure- 
ments of  their  positions  with  the  telescope  show  that  in  many  places 
in  space  large  numbers  are  grouped  in  relatively  small  volumes. 
Among  the  best-known  groups  are  the  Pleiades,  Fig.  41,  the  Hyades, 
Fig.  35,  the  Coma  Berenices,  Praecepe,  Cancer,  and  Orion.  While 
they  differ  greatly  among  themselves,  a  general  idea  of  their  enor- 


Fig.  100.     Photograph  of  the  Pleiades  Showing  the  Nebulous  Material  Which  Surrounds  the  Principal  Stare 


ASTRONOMY  221 

v 

mous  dimensions  and  splendid  character  can  be  obtained  from  a 
description  of  the  Pleiades.  The  seven  brightest  stars  of  the  Pleiades 
cover  nearly  three  square  degrees  of  the  sky  and,  as  was  stated  in 
the  discussion  of  the  constellation  Taurus,  they  are  so  far  away 
that  it  takes  their  light  nearly  300  years  to  come  to  us.  At  this 
distance  the  sun  would  appear  as  an  insignificant  ninth-magnitude 
star.  The  Pleiades  average  more  than  one  hundred  times  as  great 
as  the  sun  in  light-giving  power.  The  distances  between  the  stars 
of  this  group  are  such  that  it  requires  several  years  for  light  to  pass 
from  one  to  the  other.  Besides  the  seven  stars  which  are  visible  to 
the  unaided  eye,  the  telescope  shows  45  others  which  have  the  same 
motion  in  both  direction  and  speed  and  whose  spectra  are  similar. 
They  are  undoubtedly  a  part  of  the  same  great  family  of  stars. 
In  addition  to  these  stars  there  are  about  2,000  fainter  ones,  which 
so  far  have  not  been  examined  with  sufficient  care  to  enable  us  to 
determine  whether  they  are  really  members  of  the  same  group  or  not. 

With  the  most  powerful  instruments  and  under  good  con- 
ditions some  of  the  stars  of  the  Pleiades  are  seen  to  be  surrounded 
by  very  faint  nebulous  masses.  When  photographed  with  reflecting 
telescopes,  which  are  peculiarly  suited  for  bringing  out  the  details 
of  very  faint  and  diffuse  objects,  the  principal  stars  of  the  Pleiades 
are  seen  to  be  entirely  surrounded  by  enormous  masses  of  nebulous 
matter  reaching  almost  from  star  to  star.  Fig.  100  is  a  photograph 
of  this  region  taken  at  the  Yerkes  Observatory.  The  magnificence 
of  a  great  group  of  stars  averaging  more  than  one  hundred  times  the 
splendor  of  our  sun,  and  of  such  dimensions  that  it  takes  light  years 
to  travel  from  one  to  another,  and  all  enshrouded  in  huge  masses  of 
nebulous  material  is  enough  to  stagger  the  imagination.  Surely  these 
stars  in  a  very  real  sense  form  a  family  and  have  had  a  common  origin. 

Long  exposure  photographs  of  the  Pleiades'  region  covering 
the  neighboring  sky  show  that  surrounding  them  there  are  very 
faint  nebulosities  which  cover  a  region  more  than  10  degrees  square. 
These  nebulous  masses  are  incomparably  greater  in  extent  than 
those  which  are  shown  in  Fig.  100. 

In  addition  to  the  scattered  groups  of  stars,  such  as  the  Pleiades, 
there  are  other  groups  which  are  in  some  respects  more  wonderful. 
They  cover  very  small  portions  of  the  sky,  generally  much  less  than 
the  apparent  size  of  the  moon,  and  contain  in  these  small  areas 


222 


ASTRONOMY 


from  3,000  to  60,000  stars.  There  are  more  than  100  of  these  systems 
known,  and  they  are  found  in  all  parts  of  the  sky,  especially  in  or 
near  the  Milky  Way.  Fig.  101  shows  one  of  these  magnificent  star 
clusters  which  is  situated  in  the  constellation  Hercules.  The  stars 
in  these  clusters  are  not  only  individually  invisible  without  a  tele- 
scope, but  taken  all  together  they  can  not  be  seen  without  optical  aid. 


Fig.  101.     The  Great  Star  Cluster  in  Hercules 

They  are  generally  very  faint,  ranging  from  the  twelfth  to  the  six- 
teenth magnitude.  It  is  a  question  of  the  highest  interest  whether 
these  systems  are  made  up  of  great  suns  like  our  own,  which  appear 
feeble  and  near  together  only  because  of  their  enormous  distances 
from  us,  or  whether  they  are  small  suns  closely  crowded  together 
and  of  not  very  great  distance  from  us.  If  the  latter  hypothesis  is 


ASTRONOMY  223 

correct  they  have  had  a  peculiar  evolution  quite  different  from  that 
of  the  great  mass  of  stars.  It  has  not  been  possible  so  far  to  measure 
directly  the  distance  of  any  globular  cluster.  We  can  make  only 
an  inference  of  their  remoteness  in  the  sky  from  their  relative  fixity 
on  the  celestial  sphere.  Thus  far  observations  have  not  shown  any 
direct  motions  of  any  of  the  star  clusters.  In  one  or  two  cases  observa- 
tions have  shown  the  motions  of  an  individual  star  in  them,  but  it 
seems  probable  at  present  that  these  stars  are  only  apparently  in 
the  clusters.  It  must  be  remembered  that  since  stars  cover  rather 
thickly  nearly  the  whole  sky,  there  will  be  some  ir  the  direction  of 
the  clusters,  and  apparently  in  them,  which  do  not  actually  belong 
to  them.  If  such  a  star  were  much  nearer  to  us  than  the  cluster  a 
moderate  motion  would  give  it  the  appearance  of  moving  rapidly  in 
the  cluster*. 

To  summarize,  the  facts  are  that  no  cluster  as  a  whole  has  been 
observed  to  have  any  motion  on  the  celestial  sphere,  and  only  a  very 
few  individuals  of  certain  clusters  have  been  found  to  have  motions 
in  the  clusters  themselves.  We  infer  from  their  fixed  positions  on 
the  sky  that  they  are  actually  very  remote  from  us.  Of  course,  time 
will  reveal  their  actual  motions  and  permit  us  to  make  more  than  a 
conjecture.  At  the  present  time  it  seems  very  probable  that  they 
are  distant  at  least  400  light  years.  At  any  rate,  we  may  make  the 
assumption  in  order  to  obtain  some  sort  of  a  mental  picture  of  what 
a  cluster  really  is.  At  that  distance  our  sun  would  appear  as  an 
eleventh-magnitude  star.  If  the  assumption  is  correct,  it  follows 
that  the  stars  of  the  clusters  are  somewhat  fainter  than  our  sun 
though  comparable  to  it.  The  more  interesting  question  is  how 
far  they  are  from  one  another.  A  computation  shows  that  in  the 
star  cluster  whose  photograph  is  given  in  Fig.  101,  where  in  its  center 
the  stars  seem  to  touch  one  another  and  where  there  seems  to  be 
imminent  danger  of  collision,  the  distance  of  one  star  from  another 
is  on  the  average  30,000  times  as  far  as  the  distance  from  the  sun 
to  the  earth;  or,  in  round  numbers,  the  distance  from  one  star  to 
another  in  Fig.  101  is  30,000  times  100,000,000  miles.  Since  gravita- 
tion varies  inversely  as  the  square  of  the  distance,  it  is  not  surpris- 
ing that  the  interactions  of  these  stars  on  one  another  do  not  pro- 
duce sufficient  motions  to  be  observed  in  the  short  time  they  have 
been  followed  by  our  great  telescopes.  In  these  clusters  there  is 


224  ASTRONOMY 

abundant  room  for  almost  permanent  motion  of  the  stars  without 
any  danger  of  collisions,  and  each  sun  might  be  accompanied  by  a 
retinue  of  planets  without  their  being  in  any  particular  danger  of 
destruction  from  other  suns. 

A  remarkable  peculiarity  of  the  stars  of  some  of  the  clusters 
is  that  a  considerable  fraction  of  them  vary  in  the  light  they  radiate. 
The  period  of  variation  is  almost  the  same  for  the  variable  stars  of 
one  cluster  but  may  be  somewhat  different  for  those  of  another. 
The  periods  are  generally  about  a  day.  The  light  from  the  stars  is 
sensibly  uniform  except  for  a  short  time  when  it  flashes  out  with 
from  two  to  six  times  its  ordinary  brilliance.  More  than  500  of  this 
type  of  variables  have  so  far  been  found.  There  is  no  explanation 
for  this  most  peculiar  variability. 

Recent  measurements  of  the  distances  and  motions  of  the  stars 
show  that  our  own  sun  is  a  member  of  a  rather  open  cluster  of  per- 
haps about  100  stars.  Our  great  distance  from  all  other  suns  gives 
us  an  idea  of  the  distances  separating  the  stars  in  the  clusters. 

Double  Stars.  A  few  double  stars  have  been  known  since 
the  invention  of  the  telescope.  They  are  two  suns  which  are  so  near 
together  that  they  appear  as  a  single  one  without  an  instrument. 
In  modern  times  the  limits  are  still  closer  than  this  definition  would 
lead  one  to  infer,  for  a  star  is  not  considered  as  being  a  real  double 
unless  the  distance  separating  its  components  is  less  than  0.1  of  that 
which  is  the  limit  of  visibility  without  telescopic  aid.  There  are 
very  many  of  these  objects  known  at  the  present  time,  and  in  Burn- 
ham's  great  catalogue  of  double  stars  the  observations  and  descrip- 
tions of  about  13,000  are  given. 

Originally  it  was  supposed  that  our  sun  and  planetary  system 
is  a  type  of  all  the  systems  in  space,  and  consequently  that  double 
stars  are  simply  examples  of  two  suns  happening  to  be  in  the  same 
direction  in  space.  A  computation  shows  easily  that  the  probabili- 
ties are  against  very  many  pairs  existing  in  which  two  are  seen  almost 
exactly  in  the  same  direction  and  are  not  actually  associated.  About 
120  years  ago  Sir  William  Herschel  began  systematic  observations 
of  the  double  stars  in  order  to  determine  their  distances;  for  it  was 
clear  that  if  they  were  only  apparently  in  the  same  direction,  and  one 
many  times  as  far  away  as  the  other,  the  near  one  would  apparently 
move  with  respect  to  the  remote  one  while  the  earth  was  making  its 


ASTRONOMY 


225 


revolution  around  the  sun.  Herschel  did  not  find  what  he  was  look- 
ing for,  but  was  surprised  to  observe  after  a  few  years  that  in  some 
cases  the  two  stars  were  going  around  their  common  center  of  gravity. 
This  established  the  existence  of  systems  of  two  suns  revolving  near 
each  other,  and  furnished  a  model  quite  different  from  that  of  a 
single  sun  attended  by  a  family  of  planets. 

The  discoveries  which  Herschel's  successors  have  made  with 
modern  telescopes  have  shown  that  these  double-star  systems  are 
very  numerous,  and  the  number  known  is  constantly  being  added 
to  by  the  observations  which  are  carried  on  at  all  the  leading  obser- 
vatories. Those  stars  which  form  an  actual  physical  system  are 


Fig.  102.    The  Full  Curve  is  the  Apparent  Orbit  of  the  Companion 
of  Sirius;  the  Dotted  Curve  Its  Actual  Orbit 

called  binaries.  The  periods  of  the  binaries  range  from  about  five 
years  to  hundreds,  and  perhaps  thousands,  of  years.  The  orbits  of 
those  whose  periods  are  very  long  are,  of  course,  not  well  known 
because  of  the  short  time  covered  by  the  observations.  The  stars 
whose  periods  are  short  are  near  one  another,  and  the  stars  whose 
periods  are  long  are  on  the  whole  very  remote  from  one  another.  Fig. 
102  shows  in  a  dotted  curve  the  real  orbit  of  the  companion  of  Sirius 
with  respect  to  the  principal  star,  which  is  represented  by  a  small 
circle  where  the  axes  cross.  The  plane  of  the  orbit  is  tipped  through 
an  angle  of  about  45°  around  the  line  L.  Consequently,  instead 
of  seeing  the  companion  move  along  the  dotted  ellipse,  we  find  it 
moving  along  the  full  line  ellipse,  which  is  the  projection  of  the  other. 


226 


ASTRONOMY 


TABLE  VIII 
Binary  Stars  Whose  Masses  and  Distances  Are  Known 


Star 

Semi-axis 

Period 

Mass 

Light 

Eccentricity 

Alpha  Centauri 

23.6 

81 

2.0 

1.7 

0.53 

Siriiis 

21.7 

52 

3.7 

32.0 

0.62 

Procyon 

10.0 

40 

0.6 

8.5 

Eta  Cassiopeiae 

41.0 

196 

1.8 

1.0 

0.51 

70  Ophiuchi 

24.0 

88 

1.8 

0.7 

0.50 

85  Pegasi 

19.5 

24 

11.3 

2.2 

0.59 

The  apparent  distances  of  double  stars  from  each  other  are 
determined  by  direct  observations  with  the  telescope.  Their  actual 
distances  from  each  other  can  not  be  found  unless  their  distances 
from  the  earth  are  known.  In  a  few  cases  the  distances  of  binary 
stars  are  known,  and  in  these  cases  the  real  distances  of  the  two 
members  from  each  other  can  be  determined.  When  the  distances 
of  two  stars  from  each  other  and  their  periods  of  revolution  are  known, 
their  masses  can  be  found  just  as  the  mass  of  the  planet  can  be  found 
from  the  period  of  a  satellite  which  revolves  around  it  at  a  known 
distance  and  in  a  known  period.  Also,  when  the  distances  of  the 

stars  are  known,  their  lum- 
inosity compared  to  that  of 
the  sun  can  be  determined. 

There  is  one  striking  differ- 
ence between  the  orbits  of 
binary  stars  and  the  orbits 
of  the  planets  in  their  mo- 
tions around  the  sun.  While 
the  planetary  orbits  are 
nearly  round,  the  orbits  of  the 
binary  stars  are,  on  the  whole,  very  elongated.  The  average  eccen- 
tricity of  those  which  are  best  known  is  in  the  neighborhood  of  0.5. 
Table  VIII  gives  the  stars  whose  distances,  actual  orbits,  masses, 
and  light  in  terms  of  the  sun's  light  are  known.  In  column  one  is 
the  name  of  the  star;  in  column  two,  the  semi-axis  of  its  orbit  expressed 
in  terms  of  the  mean  distance  from  the  earth  to  the  sun;  in  column 
three,  the  period  expressed  in  years;  in  column  four,  the  mass 
expressed  in  terms  of  the  sun's  mass;  in  column  five,  the  light 


Fig.  103.     The  Shift  in  the  Spectral  Lines  of  a 
Binary  Star 


ASTRONOMY  227 

expressed  in  terms  of  the  light  radiated  by  the  sun;  and  in  column 
six,  the  eccentricity  of  the  orbit. 

Spectroscopic  Binary  Stars.  In  many  cases  there  are  two  stars 
which  are  so  remote  and  so  close  together  that  they  appear  as  one 
when  seen  through  the  most  powerful  telescopes.  The  spectroscope 
has  enabled  us  under  certain  circumstances  to  determine,  neverthe- 
less, their  binary  character.  If  a  star  is  coming  toward  us,  the  lines 
in  its  spectrum  are  shifted  toward  the  violet  end,  just  as  when  a 
locomotive  is  approaching  us  the  pitch  of  its  whistle  is  raised.  The 
approach  of  a  star  crowds  the  waves  closer  together  and  changes 
the  color  toward  the  blue  end  of  the  spectrum.  Our  eyes  are  not 
sufficiently  sensitive  to  slight  differences  in  color  to  enable  us  to 
detect  this  change,  but  it  is  possible  in  many  cases  to  measure  the 
shift  in  the  spectral  lines.  A  star  receding  has  its  lines  shifted  corre- 
spondingly toward  the  red  end  of  the  spectrum. 

Suppose  the  circle  in  Fig.  103  represents  the  orbits  of  two  equal 
stars  revolving  around  their  center  of  gravity  0  in  the  direction 
indicated  by  the  arrow  on  the  orbit.  Suppose  the  earth  is  extremely 
far  away  in  the  direction  indicated,  and  that  the  two  stars  appear 
single  as  seen  through  even  the  most  powerful  telescopes.  Suppose 
also  that  they  are  chemically  and  physically  the  same,  so  that  they 
have  like  spectra.  Consider  the  system  when  one  star  is  at  A 1  and 
the  other  at  Bt.  In  this  position  the  star  at  A±  is  receding  from  the 
earth  and  the  star  at  Bl  is  approaching  toward  it  at  an  equal  rate. 
Therefore,  the  spectrum  of  the  star  Al  will  be  shifted  toward  the 
red,  and  the  spectrum  of  the  star  B±  correspondingly  toward  the 
violet.  The  spectrum  then  will  be  composed  of  double  lines  whose 
distance  apart  will  depend  upon  the  relative  velocities  of  the  stars. 
For  the  velocities  which  are  actually  found  the  lines  are  always  very 
close  together. 

Now,  consider  the  system  again  when  A±  has  moved  forward 
to  A 2  and  Bl  to  B2.  In  this  position  the  stars  are  neither  approach- 
ing nor  receding  and  their  lines  all  appear  single.  When  Al  and  Bt 
have  changed  places  the  lines  again  appear  double.  The  period  of 
revolution  is  the  time  between  the  one  doubling  of  the  lines  to  the 
second  following  doubling. 

In  this  way  the  existence  of  binary  stars  is  not  only  proved,  but 
it  is  possible  to  find  out  more  about  the  orbits  than  is  generally  the 


228  ASTRONOMY 

case  in  ordinary  visual  binaries.  The  spectroscope  shows  not  only 
the  periods,  but  the  velocities,  of  the  stars  in  their  orbits,  from  which 
we  can  compute  their  actual  dimensions.  Knowing, the  dimensions 
of  the  orbits  and  the  periods,  the  masses  can  be  found.  The  spec- 
troscopic  observations  do  not  enable  us  to  determine  the  distances 
of  the  stars  from  us  and,  therefore,  we  cannot  determine  their 
brightness. 

Besides  the  spectroscopic  binaries  of  the  type  just  described, 
there  are  many  others  in  which  one  of  the  two  stars  is  so  faint  that 
its  spectrum  can  not  be  observed.  In  such  cases  the  star  whose 
spectrum  is  visible  shifts  alternately  toward  the  violet  and  the  red 
ends  of  the  spectrum.  The  period  of  the  shift  shows  the  period  of 
revolution  of  the  pair,  and  the  amount  of  shift  shows  the  dimensions 
of  the  orbit  of  the  brighter  star.  It  is  not  possible  in  this  case  to 
determine  the  exact  masses  because  this  determination  depends 
upon  the  distance  of  the  stars  from  each  other,  and  this  can  not  be 
determined  from  the  distance  of  one  alone  from  its  center  of  gravity. 
A  sort  of  lower  limit  to  the  masses  can  be  found  because  the  distances 
of  the  stars  from  each  other  must  be  greater  than  that  of  the  more 
luminous  one  from  its  center  of  gravity,  and  in  general  will  be  more 
than  twice  that  great. 

There  is  another  uncertain  factor  in  the  determination  of  these 
orbits,  viz,  the  angle  which  the  plane  of  the  orbits  makes  with  a  line 
joining  the  stars  with  the  earth.  In  the  diagram  and  in  the  discus- 
sion so  far  it  has  been  assumed  that  the  plane  of  their  orbit  passes 
through  the  earth.  It  is  obvious  that  in  general  it  will  be  inclined 
to  the  line  from  the  stars  to  the  earth.  Consequently,  instead  of 
having  the  total  velocity  of  the  stars  in  the  case  of  the  double  lines, 
we  shall  have  only  that  component  which  is  toward  the  earth.  This 
leads  us  in  general  to  a  too  small  value  for  the  combined  masses  of 
the  system. 

The  study  of  binary  stars  by  means  of  the  spectroscope  was 
begun  in  1889  and  most  of  the  work  in  it  has  been  done  since  1900. 
In  1905  there  were  136  spectroscopic  binaries  known,  and  on  January 
21,  1910,  there  were  306.  The  number  of  orbits  of  those  which  are 
fairly  well  determined  is  now  about  70.  The  periods  range  from  less 
than  five  hours  up  to  nearly  two  years.  The  distances  apart  of  the 
components  vary  from  50,000  miles  as  a  lower  limit  to  nearly 


ASTRONOMY  229 

105,000,000  miles.  The  eccentricities  vary  from  practically  zero  to 
about  0.9.  On  the  whole  the  stars  with  the  shorter  periods  have 
the  smaller  eccentricities. 

Variable  Stars.  The  variability  in  the  light  of  certain  stars  in 
the  globular  clusters  was  mentioned  above.  There  are  many  other 
stars  whose  light  varies  in  different  ways.  The  first  one  known  was 
Omicron  Ceti,  discovered  in  1596.  The  next  one  was  Algol  (the 
Demon),  discovered  in  1783.  Variable  stars  were  not  known  in  any 
considerable  numbers  until  near  the  close  of  the  nineteenth  century, 
and  now  more  than  three  hundred  of  these  objects  are  in  the  cata- 
logues. 

In  one  type  of  variables  the  light  of  a  star  remains  constant 
except  for  short  intervals  when  it  diminishes  greatly  in  brightness.  The 
typical  star  of  this  type  is  Algol,  and  there  are  about  twenty-five  such 
stars  known.  Their  periods  are  generally  less  than  five  days.  The 
explanation  of  their  variability  is  that  they  consist  of  two  stars,  one 
of  which  is  relatively  dark,  revolving  around  their  center  of  gravity 
in  a  plane  passing  through  the  earth.  The  bright  star  shines  with  its 
customary  brightness  except  when  the  dark  star  passes  between 
the  luminous  one  and  the  earth,  and  then  its  light  greatly  diminishes. 
It  is  obvious  that  these  systems  are  in  most  respects  analogous  to 
the  spectroscopic  binaries  and,  indeed,  in  most  if  not  in  all  cases  the 
lines  of  the  brighter  component  shift  in  a  way  which  proves  their 
binary  character.  The  star  Algol  has  a  period  of  two  days,  28  hours, 
48  minutes,  and  55  seconds.  It  is  normally  a  star  of  the  second  mag- 
nitude, but  at  the  time  of  eclipse  it  loses  five-sixths  of  its  light.  This 
is  a  spectroscopic  binary  and  the  orbit  of  the  brighter  component  is 
consequently  known.  Its  distance  from  the  center  of  gravity  of  the 
system  is  about  1,000,000  miles.  From  the  duration  of  the  eclipse 
and  the  rate  at  which  the  light  fades  and  returns,  it  is  possible  to 
compute  the  diameters  of  the  bright  and  faint  stars.  In  the  case  of 
this  star  the  bright  component  has  a  diameter  of  approximately 
1,000,000  miles  and  the  dark  component  800,QOO  miles.  From  meas- 
urements of  the  distance  of  this  pair,  which  unfortunately  are  sub- 
ject to  some  error,  it  is  found  that  the  bright  component  radiates 
80  times  as  much  light  as  our  sun.  Taking  into  account  the  area 
of  its  surface,  it  follows  that  it  radiates  52  times  as  much  light  per 
unit  area  as  the  sun  does. 


230  ASTRONOMY 

There  are  several  slight  variations  from  the  type  exemplified 
by  Algol.  One  is  that  in  which  the  stars  are  of  unequal  size  but 
both  bright.  Then  each  eclipses  the  other  in  turn  during  their 
revolution.  The  star  Beta  Lyrae  is  an  example  of  another  type 
closely  related  to  the  Algol  variables.  The  chief  differences  are 
that  the  light  varies  continuously  from  its  maximum  to  its  mini- 
mum and  back  to  its  maximum  again.  There  are  generally  two 
minima  and  a  single  maximum.  The  explanation  of  these  stars  is 
that  the  two  components  revolve  very  near  together  and  in  a  plane 
passing  through  the  earth.  Under  these  circumstances  as  soon  as 
the  first  star  passes  out  of  its  eclipse  by  the  second,  it  immediately 
begins  to  eclipse  the  second.  One  minimum  is  when  the  fainter  is 
between  the  earth  and  the  brighter,  and  the  other  minimum  is  when 
the  brighter  is  between  the  earth  and  the  fainter.  Of  course,  if  the 
two  were  equal  in  all  respects  there  would  be  a  single  minimum. 
The  maximum  is  when  the  line  joining  the  stars  is  at  right  angles 
to  the  line  joining  them  with  the  earth,  at  which  time  the  earth 
receives  the  full  light  of  both  of  them.  These  stars  have  been  found 
from  the  variation  of  light  and  the  shifts  of  their  spectral  lines  to 
be  of  enormous  dimensions  and  very  tenuous. 

There  is  another  type  of  variable  stars  of  which  Omicron  Ceti 
is  the  best-known  example.  This  star  has  been  observed  through 
more  than  300  of  its  cycles.  The  periods  of  these  stars  are  long  and 
irregular.  The  time  for  minimum  to  maximum  is  generally  con- 
siderably shorter  than  from  maximum  to  minimum.  The  maxima 
and  minima  are  subject  to  great  irregularities,  and  there  is  no  dis- 
coverable relation  of  them  to  the  period.  According  to  the  observa- 
tions of  Sir  William  Herschel  the  star  Omicron  Ceti  changed  its  light 
more  than  10,000  fold  in  only  four  years.  The  spectroscope  showed 
marked  changes  in  the  spectra  of  these  stars,  but  no  evidence  of 
their  being  spectroscopic  binaries.  They  are  generally  red  stars 
which  seem  far  advanced  in  their  cooling,  but  we  can  imagine  no  inter- 
nal disturbances  which  would  cause  the  enormous  fluctuations  in 
their  radiating  power  that  is  often  observed. 

There  are  besides  the  stars  of  the  Omicron  Ceti  type  others 
whose  variations  give  no  hint  of  periodicity.  Some  are  characterized 
by  their  light  suddenly  flashing  out  with  great  brilliance,  usually 
after  intervals  of  many  years  of  quiescence,  and  others  unaccount- 


ASTRONOMY  231 

ably  fade  away  and  become  invisible  even  through  the  most  power- 
ful telescopes.  These  stars  are  also  generally  red  and  sometimes 
apparently  associated  with  faint  nebulous  masses. 

Temporary  Stars.  Occasionally  stars  have  been  observed  to 
blaze  forth  suddenly  in  parts  of  the  sky  (so  far  always  in  the  Milky 
Way)  where  none  had  previously  been  seen,  and  then  to  sink  away 
quickly  into  obscurity.  They  are  characterized  by  a  very  sudden 
rise  to  a  great  maximum  which  in  spite  of  later  possible  increases 
is  never  repeated.  One  of  the  most  remarkable  of  these  was  observed 
in  Cassiopeia  in  1572,  and  was  mentioned  in  the  discussion  of  this 
constellation. 

One  of  the  recent  remarkable  stars  of  this  type  appeared  in  1901 
in  the  constellation  Perseus.  On  February  19  of  that  year  a  photo- 
graph of  the  region  where  it  later  appeared  was  taken  and  did  not 
show  it.  By  the  23d  it  was  brighter  than  the  star  Capella.  In  this 
short  interval  its  light  had  increased  more  than  20,000  fold.  A  day 
later  it  had  lost  one-third  of  its  light,  and  it  steadily  decreased  in 
brightness  until  about  the  22d  of  March,  when  it  flashed  up.  It 
then  diminished  again  until  the  24th  of  April,  when  it  had  gone  down 
to  the  sixth  magnitude.  At  this  time  it  flashed  up  again  nearly  to 
the  third  magnitude,  after  which  it  faded  away  and  became  entirely 
invisible  by  the  end  of  the  year. 

The  explanation  of  these  temporary  stars  is  that  they  are  dark 
suns  moving  swiftly  through  space  and  that  they  suddenly  encounter 
invisible  dust  clouds  or  nebulous  material.  Striking  these  tenuous 
masses  with  high  speed,  their  surfaces  are  suddenly  made  to  glow 
with  a  brilliant  light  analogous  .to  that  of  the  tiny  meteors  when 
they  dash  into  our  atmosphere.  Since  the  surface  only  is  heated 
the  light  speeclily  fails  when  the  star  passes  through  the  material 
with  which  it  collides.  Secondary  collisions  with  dark  masses  of  the 
dust  clouds  or  nebulous  material  cause  the  secondary  flashes  that 
sometimes  are  observed  in  these  stars.  The  star  Nova  Persei  was 
photographed  a  few  months  after  it  blazed  forth  and  was  found  to 
be  surrounded  by  a  very  faint  nebulous  mass.  The  explanation  is 
that  the  nebulous  matter  which  had  previously  been  dark  and 
invisible,  became  visible  as  it  was  lighted  up  by  the  glowing  star. 
The  star  Nova  Persei  was  so  far  from  us  that  it  took  its  light  approxi- 
mately 300  years  to  reach  us.  This  means  that  the  collision,  instead 


Fig.   104.     Primitive  Nebulous  Material  in  Cygnus.     Photographed  at  the   Yerkes  Observatory 


ASTRONOMY 


233 


of  taking  place  in  1901  when  the  star  was  observed,  actually  took 
place  about  the  year  1600. 

Nebulas.  Scattered  here  and  there  throughout  space  are  great 
cloud  masses  of  low  luminosity  known  as  nebulas.  They  are 
supposed  to  be  the  primitive  world  stuff  out  of  which  suns  are 
made  in  very  early  stages  of  their  development.  Fig.  104  is  a  photo- 


Fig.  105.     The  Trifid  Nebula 

graph  of  an  extremely  widespread,  gauze-like,  nebulous  mass  which 
is  so  faint  that  it  is  visible  only  in  a  very  large  telescope.  This  is 
about  the  most  primitive  type  of  world  stuff  with  which  we  are 
acquainted.  It  suggests  that  the  process  of  creation,  or  .of  evolution 
of  matter  from  something  more  primitive,  was  not  an  event  which 
took  place  at  any  one  time  and  then  stopped,  but  rather  one  which 


234 


ASTRONOMY 


always  has  been  and  always  will  be  taking  place.  That  is,  these 
photographs  suggest  that  creation  is  a  process  continuously  going 
on  rather  than  one  confined  to  any  particular  time.  If  this  idea  is 
correct  the  nebula  whose  photograph  is  shown  in  Fig.  104,  is  matter 
recently  created,  using  recently  in  the  astronomical  sense. 


Fig.  106.     A  Spiral  Nebula  in  Ursa  Major 

There  are  other  nebulas  which  show  a  considerably  higher 
degree  of  organization  of  matter  as,  for  example,  that  in  Orion, 
Fig.  43.  There  are  others  still  farther  advanced,  as  shown  in  Fig. 
105.  In  addition  to  these  more  or  less  irregular  nebulous  masses, 
there  are  the  spirals  which  exhibit  a  high  degree  of  organization  and 
to  which  we  shall  have  occasion  to  refer  in  discussing  the  origin  and 
evolution  of  the  solar  system.  Fig.  106  shows  one  of  these  spiral 


ASTRONOMY  235 

nebulas  which  is  in  the  constellation  Ursa  Major.  There  are  still 
others  associated  with  stars;  and  some,  called  "planetary  nebulas," 
have  the  general  appearance  of  a  planet. 

All  the  nebulas  except  the  spirals  have  bright-line  spectra 
instead  of  dark-line  spectra  like  those  of  the  sun  and  stars.  This 
shows,  in  accordance  with  the  principles  of  spectrum  analysis,  that 
the  nebulas  are  masses  of  incandescent  gas  rather  than  luminous 
solids  or  liquids  shining  through  cooler  gases.  Before  these  results 
were  obtained  by  the  spectroscope  it  was  supposed  that  perhaps 
the  nebulas  were  other  galaxies  of  stars  so  far  away  that  their  individ- 
ual members  were  not  separately  visible.  The  spectroscope,  how- 
ever, proves  they  are  gaseous  and  this  conclusion  is  in  harmony 
with  other  considerations  regarding  the  evolution  of  suns. 

COSMOGONY,  OR  THE  EVOLUTION  OF  WORLDS 

Evolution.  A  slow  change  in  one  direction,  especially  if  it 
be  from  the  simple  and  unorganized  to  the  complex  and  organized, 
is  said  to  be  an  evolution.  The  central  idea  of  it  is  that  the  change 
from  one  state  to  another  is  an  orderly  and  continuous  one  rather 
than  a  chaotic  and  abrupt  one.  When  considered  in -this  way  it  is 
seen  that  evolution  is  simply  a  statement  that  the  organization  of 
the  universe  which  makes  science  possible  is  extensive  in  time  as 
well  as  in  space. 

In  order  to  discover  the  evolution  of  any  part  of  the  physical 
universe  it  is  necessary  to  know  the  condition  of  it  at  a  given  instant 
and  the  laws  according  to  which  it  changes.  For  example,  in  order 
to  determine  the  evolution  of  the  solar  system  we  must  know  its 
condition  at  one  time  and  how  its  various  members  change.  In  the 
preceding  pages  a  description  of  the  solar  system  has  been  given 
and  a  synopsis  of  the  chief  laws  which  it  obeys.  If  all  of  the  data 
and  all  of  the  laws  of  change  were  known,  and  if  one  possessed 
sufficiently  powerful  mathematical  processes  for  making  the  solu- 
tion, then  it  would  be  possible  to  predict  the  condition  of  the  solar 
system  for  indefinite  time  in  the  future,  and  to  find  what  it  had 
been  for  indefinite  time  in  the  past.  Unfortunately,  we  are  never 
able  to  determine  fully  all  the  factors  which-  are  involved  in  a  series 
of  changes,  and  it  is  equally  certain  that  we  do  not  know  with 
absolute  exactness  all  of  the  laws  to  which  the  system  is  subject. 


236  ASTRONOMY 

For  example,  the  temperature  of  a  given  place  on  the  earth 
depends  upon  the  temperature  and  the  distance  of  the  sun,  the  way 
the  distance  from  the  earth  to  the  sun  changes,  the  period  of  the 
earth's  rotation,  and  many  other  factors.  A  great  many  of  the 
determining  factors  are  known  exactly,  or  at  least  with  a  high  degree 
of  precision,  but  some  are  totally  unknown.  If  the  most  important 
of  them  are  known  with  a  considerable  degree  of  accuracy,  predic- 
tions can  be  made  with  corresponding  accuracy  even  though  some 
of  them  remain  unknown.  Thus,  in  the  case  of  the  temperature  of 
the  place  just  mentioned,  while  many  factors  are  unknown,  predic- 
tions which  are  on  the  whole  reliable  can  be  made  on  the  basis  of 
those  which  are  known.  For  ages  to  come  the  succession  of  seasons 
and  of  day  and  night  at  any  one  place  can  be  accurately  described. 
But  it  is  not  possible  to  predict  the  precise  temperature  changes  even 
for  a  short  time.  Thus,  we  see  that  while  it  is  possible  to  work  out 
a  general  idea  of  the  nature  of  the  temperature  changes,  it  is  not 
possible,  because  of  the  imperfections  of  our  knowledge,  to  describe 
them  with  absolute  precision.  The  degree  of  accuracy  decreases 
as  a  rule  with  the  extent  of  time  over  which  our  predictions  extend. 
The  chief  reason  is  that  there  may  be  certain  factors  at  work  which 
are  unknown  and  relatively  insignificant  for  a  short  time,  but  which 
in  the  long  run  become  very  important.  Thus,  in  the  case  of  the 
climate  at  a  particular  point  of  the  earth,  we  can  predict  the  changes 
of  seasons  and  of  day  and  night  and  the  mean  temperatures  with  a 
considerable  degree  of  accuracy  for  a  short  and  also  for  a  very  long 
time  if  we  know  all  the  factors  involved.  But  if  there  is  some  unknown 
cause  which  will  continually  lower  the  temperature  of  the  sun  at  a 
very  slow  rate,  then  our  predictions  will  be  almost  true  only  until 
sufficient  time  has  elapsed  for  this  unknown  cause,  operating  in  one 
direction,  to  produce  important  results. 

A  theory  of  evolution  is  extremely  valuable  in  many  ways  and 
at  the  present  time  is  considered  as  having  a  legitimate  place  in  the 
discussion  of  every  science.  In  the  first  place,  it  shows  us  what 
facts  are  important  and  what  are  not,  because,  in  attempting  to 
develop  a  theory  of  the  changes  through  which  a  system  goes,  we 
must  relate  all  the  facts  to  one  another.  If  there  are  any  contra- 
dictions among  them,  and  among  minor  theories  based  upon  them, 
they  will  be  revealed  in  our  attempts  to  weave  all  of  them  together 


ASTRONOMY  237 

into  one  systematic,  harmonious  whole.  For  example,  if  our  con- 
clusion, based  on  more  or  less  uncertain  observations,  that  Mercury 
has  one  face  always  toward  the  sun  contradicts  something  funda- 
mental in  the  system,  we  should  be  likely  to  find  it  out  in  the  con- 
sideration of  its  evolution.  Therefore,  if  we  are  considering  only 
the  facts  and  minor  conclusions  regarding  any  domain  of  science, 
we  see  that  the  attempt  to  construct  for  it  a  theory  of  evolution  is 
of  the  highest  importance  because  it  compels  a  more  careful  examina- 
tion of  these  things  which  we  are  supposing  are  important. 

In  a  somewhat  similar  manner  the  consideration  of  a  question 
in  a  large  way  often  directs  our  attention  to  gaps  in  our  knowledge 
which  ought  to  be  filled.  In  the  biological  sciences  the  theory  of  evolu- 
tion has  directed  inquiry  in  thousands  of  directions  to  supply  addi- 
tional data.  While  this  has  not  been  true  in  astronomy  to  the  same 
extent,  yet  the  theory  of  evolution  has  there  raised  many  new  ques- 
tions and  stimulated  important  investigations. 

A  theory  of  evolution  is  also  valuable  in  that  by  discovering 
what  the  conditions  will  be  in  the  future  it  makes  it  possible  for  us 
to  adjust  ourselves  to  them,  or  in  some  cases  to  control  events  for 
our  good.  An  example  of  this,  a  matter  of  such  universal  experience 
that  it  has  become  commonplace,  is  that  in  the  summertime  we  pre- 
pare for  the  winter  because  we  know  that  it  is  sure  to  come.  In  a 
larger  way,  particularly  in  the  biological  sciences,  it  may  be  possible 
to  foresee  things  in  the  remote  future  for  which  we  as  a  race  should 
prepare  ourselves. 

Finally,  a  theory  of  evolution  is  of  importance  for  the  satis- 
faction it  gives  in  contemplating  the  subject  as  one  grand  whole. 
It  is  related  to  separate  facts  and  minor  theories  upon  which  it  is 
based  as  a  beautiful  and  finished  house  is  to  unsightly  heaps  of  stone, 
brick,  and  wood  from  which  it  might  be  built.  Laplace  commenting 
on  the  satisfaction  obtained  in  considering  astronomy  as  a  unit, 
said:  "Contemplated  as  one  grand  whole  it  is  the  most  beautiful 
monument  of  the  human  mind,  and  the  noblest  record  of  its  intel- 
ligence." 

Historical.  The  theory  of  the  evolution  of  the  solar  system, 
and,  indeed,  of  all  the  stars  that  fill  the  sky,  was  first  begun  in  what 
would  now  be  considered  an  approximately  scientific  manner  by 
Thomas  Wright  of  Durham,  England,  who  published  a  volume  on 


238  ASTRONOMY 

this  subject  in  1750.  He  supposed  that  the  Milky  Way  was  com- 
posed of  a  vast  number  of  solar  systems  similar  to  our  own,  spread 
out  in  a  great  double  ring  which  rotated  around  an  axis  perpendicular 
to  its  plane.  He  treated  the  solar  system  as  an  example  illustrating 
the  dynamics  of  the  sidereal  system.  His  work  was  not  adequately 
based  on  observations  and  contained  many  serious  errors.  This, 
of  course,  was  only  to  be  expected  in  pioneer  work  in  so  difficult  a 
subject. 

The  work  of  Wright  fell  into  the  hands  of  the  brilliant  phi- 
losopher Kant,  who  was  then  a  young  man.  His  vivid  imagination 
quickly  ran  beyond  the  bounds  of  what  Wright  had  set  forth.  He 
saw  some  of  the  weaknesses  of  Wright's  theory  and  the  possibility 
of  adding  greatly  to  it.  In  1755,  he  published  a  book  on  the  subject 
agreeing  in  many  respects  with  that  of  Wright,  but  which,  on  the 
whole,  was  vastly  superior  to  it.  He  supposed  that  in  the  beginning 
all  the  material  which  now  makes  up  the  sun  and  planets  and  other 
members  of  the  solar  system  was  in  a  widely-scattered  primitive 
condition  of  un-united  elements.  He  supposed  that  the  chemical 
affinity  of  one  element  for  another  caused  compounds  to  be  formed, 
thus  setting  up  motions.  As  atom  united  with  atom  to  make  com- 
pounds, so  molecule  united  with  molecule  under  gravitative  forces 
and  made  continually  larger  and  larger  masses.  As  masses  of  con- 
siderable dimensions  were  formed  so  that  they  became  strong  centers 
of  attraction,  considerable  motions  were  developed.  In  some  obscure 
way  he  supposed  the  motions  in  all  directions,  except  that  in  which 
the  planets  moved,  were  destroyed  by  collisions,  leaving  a  number 
of  planets  revolving  in  a  definite  plane.  Kant  considered  in  succes- 
sive chapters  of  his  book  the  densities  and  rotations  of  the  planets, 
the  eccentricities  of  the  orbits,  the  origin  of  comets,  the  origin  of 
satellites,  the  origin  of  the  rings  of  Saturn,  the  zodiacal  light,  and 
the  theory  of  the  constitution  and  condition  of  the  sun. 

The  beauty  and  generality  of  Kant's  theory,  as  well  as  the 
attractive  manner  in  which  he  set  it  forth,  are  very  enticing,  but 
when  considered  calmly  in  the  light  of  modern  knowledge,  particu- 
larly in  the  light  of  dynamics,  it  is  found  to  have  some  serious  and 
fatal  faults.  Notwithstanding  this,  there  are  many  very  valuable 
contributions  in  it  to  the  subject,  and  it  is  a  stimulating  book  to  read 
even  at  the  present  time. 


ASTRONOMY  239 

The  world  was  not  prepared  for  the  ideas  of  evolution  in  1755, 
and  the  work  of  Kant  attracted  only  very  little  attention.  But  in 
1796  a  great  French  astronomer,  named  Laplace,  at  the  end  of  a 
charming  popular  book  on  astronomy,  explained  in  a  few  pages 
his  ideas  of  how  the  solar  system  may  have  arrived  at  its  present 
condition.  This  was  written  apparently  without  any  knowledge 
on  the  part  of  Laplace  of  the  work  of  either  Wright  or  Kant.  *  Laplace 
introduced  the  discussion  by  calling  attention  to  the  remarkable 
regularities  in  the  solar  system.  He  commented  on  the  fact  that  the 
planets  all  revolved  around  the  sun  in  the  same  direction  nearly  in 
the  same  plane.  He  calculated  that  this  condition  would  be  the 
result  of  chance  only  once  in  some  500,000,000  cases,  showing,  there- 
fore, that  in  all  probability  it  was  due  to  some  initial  state  from  which 
it  had  systematically  developed.  He  likewise  called  attention  to 
the  remarkable  circularity  of  the  orbits  and  the  directions  of  rotation 
of  the  planets,  etc. 

In  outline  the  theory  of  Laplace  is  that  originally  the  solar  atmos- 
phere was  a  nebulous  envelope  in  an  intensely  heated  condition, 
and  that  it  extended  oat  beyond  the  orbit  of  the  farthest  planet. 
He  supposed  the  whole  mass  rotated  as  a  solid  in  the  direction  in 
which  the  planets  now  revolve.  It  was  supposed  in  this  theory  that 
the  dimensions  of  the  system  were  maintained  by  gaseous  expansion 
the  same  as  the  dimensions  of  the  sun  or  the  earth's  atmosphere  are 
at  present.  This  great  nebulous  mass  would  lose  heat  by  radiation 
into  space  and  consequently  would  contract. 
If  such  a  rotating  mass  contracted,  it  would 
continually  rotate  faster  and  faster  for  the 
reasons  set  forth  in  discussion  of  the  question 
of  the  uniformity  of  the  earth's  rotation.  If 
a  mass  rotates  faster,  the  tendency  for  the 
material  at  its  equator  to  fly  off  because  of  the 
centrifugal  acceleration  continually  increases. 
Laplace  said  .that  it  seemed  reasonable  that 
the  contracting  solar  mass  would  reach  such  Orpianetsthe 

a  state  that  this  tendency  of  the  particles  at 

its  equator  to  fly  out  would  exactly  balance  their  tendency  to  go  in 
because  of  the  attraction  of  the  mass  interior  to  it.  When  this  state  was 
reached  he  supposed  a  ring  would  be  left  off,  as  is  indicated  in  Fig.  107. 


240  ASTRONOMY 

Unless  the  ring  were  perfectly  circular  and  uniform,  and  sub- 
ject to  no  disturbing  influences,  it  would  have  a  tendency  to  break, 
Laplace  thought,  at  some  place  and  to  concentrate  on  the  place  in 
it  where  there  was  the  greatest  mass.  That  is,  if  there  were  a  nucleus 
on  it  at  any  point,  this  excess  of  matter  would  gradually  draw  to  it 
all  the  rest  of  the  whole  ring,  while  it  would  continue  to  revolve 
around  the  sun  in  the  same  period  as  the  ring  did  at  the  time  it  was 
abandoned.  It  seemed  to  him  probable  that  the  sun  would  go  on 
shrinking  after  a  ring  was  abandoned  and  that  it  would  later  leave 
off  another,  and  then  still  another  similarly,  until  it  either  arrived 
at  a  state  of  permanent  equilibrium  or  had  a  density  so  great  that 
it  could  no  longer  contract. 

Laplace  then  supposed  the  system  of  planets  grew  up  from 
a  system  of  rings  abandoned  successively  by  the  sun,  beginning 
with  the  outermost  and  ending  with  the  innermost.  The  rings  con- 
centrating would  give  rise  to  large,  globular  masses  revolving  around 
the  sun  at  their  respective  distances  from  it.  These  globular  masses 
might  in  turn  be  rotating  so  rapidly  that  they  would  abandon  rings 
which  in  a  similar  manner  would  give  rise  to  satellites.  He  sup- 
posed that  perhaps  Saturn's  rings  were  examples  of  this  process  in 
which  the  satellites  were  not  yet  formed. 

This  theory  of  Laplace  pictures  the  earth  as  being  at  one  time 
in  a  gaseous  state.  It  was  supposed  that  by  losing  heat  it  cooled 
off  until  a  crust  formed  over  its  surface,  leaving  the  liquid  interior; 
and  it  was  thought  that  the  volcanoes  were  openings  through  the 
shallow  crust  into  that  liquid  interior.  This  theory  was  widely 
accepted:  first,  because  of  the  great  name  of  its  author;  and  second, 
because  of  its  simplicity  and  harmony  with  the  main  facts  of  the 
system.  It  gave  the  geologists  reasons  for  believing  that  the  earth 
is  very  old,  and  encouraged  them  to  draw  conclusions  respecting 
its  age  and  evolution  on  the  basis  of  geological  facts.  The  half 
century  following  Laplace's  work  was  characterized  by  most  remark- 
able activities  in  geological  science.  The  great  age  of  the  earth  was 
fully  established,  and  the  innumerable  fossils  which  filled  the  old 
rocks  were  brought  to  light  in  vast  numbers.  The  work  of  the 
geologists  paved  the  way  for  the  zoologists.  In  1858,  Darwin  extended 
the  general  ideas  of  evolution,  which  had  their  origin  in  astronomy 
and  which  had  spread  to  geology,  to  the  biological  sciences  by  his 


ASTRONOMY  241 

publication  of  the  "Origin  of  Species."  It  is  questionable  whether 
any  other  work  of  modern  times  has  had  so  profound  an  influence  on 
the  thought  of  the  world  as  this  book  by  Darwin.  Since  its  publica- 
tion the  doctrine  of  evolution,  aside  from  the  details  of  its  precise 
mode,  has  been  almost  universally  adopted.  Not  only  is  science 
considered  from  the  point  of  view  of  a  changing  universe,  but  history 
is  interpreted  in  the  light  of  it  and  its  applications  are  extended  to 
the  political  and  social  sciences,  and  even  to  religion. 

Test  of  the  Laplacian  Theory.  There  are  two  general  ways 
of  testing  the  truth  of  a  theory.  One  is  the  determination  of  whether 
it  is  consistent  with  itself,  and  the  other  is  whether  it  is  in  harmony 
with  the  facts  given  by  observations.  The  former  is  generally  the 
more  difficult  of  the  two,  and  in  questions  of  physical  science  is 
largely  of  a  mathematical  nature. 

As  Laplace  himself  pointed  out,  his  hypothesis  as  to  the  ring 
origin  of  the  planets  is  in  agreement  with  the  chief  facts  of  the  solar 
system.  If  the  solar  system  originated  in  this  fashion  we  should 
expect  all  the  planets  to  be  revolving  in  the  same  plane,  or  at  least 
nearly  in  the  same  plane,  and  such  is  the  case.  If  there  were  any 
deviations  from  strict  agreement  of  the  planes  of  revolution  due  to 
any  irregularities  in  the  original  solar  nebula,  we  should  expect  to 
find  the  greatest  ones  in  the  planets  far  from  the  sun,  because  as  the 
sun  continued  to  rotate  there  would  be  a  tendency  for  it  to  become 
more  and  more  uniform.  Here  the  consequences  of  the  theory  are 
not  so  well  in  harmony  with  the  facts,  for  the  orbits  of  the  remote 
planets  are  on  the  whole  much  more  nearly  circular  than  those  which 
are  closer  to  the  sun.  Mercury  has  a  more  eccentric  orbit  than  any 
other  planet.  According  to  this  theory  the  planets  should  all  revolve 
around  the  sun  in  the  same  direction,  and  this  is  found  to  be  true 
in  the  solar  system.  According  to  the  Laplacian  theory  the  orbits 
should  be  very  nearly  if  not  exactly  circular,  and  this  is  also  almost 
verified  in  the  solar  system.  If  there  were  any  deviations  from  sensible 
circularity  it  would  be  expected,  according  to  the  theory,  that  they 
would  be  the  greatest  in  the  case  of  the  orbits  of  those  planets  which 
Were  far  from  the  sun.  Here  the  theory  is  not  in  so  perfect  harmony 
with  the  facts,  because  it  is  found  that  the  orbits  of  the  remote 
planets  are  on  the  average  more  nearly  circular  than  those  closer  to 
the  sun,  and  that  Mercury's  orbit  is  the  most  elongated  of  all. 


242  ASTRONOMY 

While  the  Laplacian  theory  is  in  general  harmony  with  the  main 
facts  furnished  by  observation,  there  are,  nevertheless,  some  respects 
in  which  it  is  not  entirely  satisfactory.  The  question  arises  whether 
they  are  not  sufficient  to  compel  us  radically  to  modify  it.  It  is 
understood  that  it  is  easier  to  disprove  a  theory  which  is  wrong  than 
it  is  to  establish  one  which  is  correct,  for  one  example  contradictory 
to  an  erroneous  theory  disproves  it,  while  many  examples  of  harmony 
with  a  correct  theory  only  show  that  it  is  probable.  A  slight  dis- 
agreement between  the  ring  theory  and  the  planes  of  the  orbits  of 
the  planets  and  their  eccentricities  have  been  noted.  There  is  much 
more  serious  disagreement  when  we  come  to  a  consideration  of  the 
orbits  of  the  planetoids,  which  were  not  known  when  Laplace  first 
formulated  his  theory.  There  are  now  about  700  known  planetoids 
whose  orbits  vary  from  coincidence  with  the  plane  of  the  planetary 
orbits,  to  an  inclination  of  nearly  40  degrees  to  it,  and  from  sensibly 
perfect  circularity  to  elongations  nearly  as  great  as  those  of  some  of 
the  cometary  orbits.  These  700  orbits  weave  in  and  out  among  one 
another  in  such  a  fashion  that  if  they  were  made  of  wire  one  could 
not  be  removed  without  taking  all  of  them.  According  to  the  ring 
theory  it  is  necessary  to  suppose  that  a  ring  was  abandoned  for  each 
one  of  them.  It  is  perfectly  obvious  that  so  complex  a  ring  system 
intersecting  itself,  is  entirely  outside  of  the  possibilities.  For  example, 
the  orbit  of  Eros  reaches  out  beyond  that  of  Mars  and  down  almost 
to  that  of  the  earth,  and  is  highly  inclined  to  the  orbits  of  both  planets. 
The  ring  theory  asks  us  to  suppose  that  a  ring  was  abandoned,  which 
later  went  into  the  planet  Mars,  then  another  highly  inclined  to  the 
former  and  reaching  beyond  it,  which  went  into  the  planetoid  Eros, 
and  then  another  from  which  the  earth  developed.  The  impossi- 
bility is  apparent. 

Objections  of  quite  another  type  are  presented  in  the  case  of 
the  satellites  of  Saturn  and  Jupiter.  Each  of  these  planets  has  a 
single  satellite  revolving  around  it  in  the  retrograde  direction. 
According  to  the  Laplacian  theory  of  the  origin  of  the  satellites, 
rings  were  abandoned  at  their  respective  distances  and  the  planetary 
nebula  contracting  later  abandoned  more  rings.  It  follows  from 
this  theory  that  all  the  satellites  must  necessarily  revolve  around 
their  respective  planets  in  the  same  direction.  The  fact  that  this 
is  not  so  in  two  cases  is  a  direct  contradiction  of  the  theory. 


ASTRONOMY  243 

It  has  been  stated  that  as  a  body  contracts  it  rotates  faster 
and  faster.  Consequently,  since  by  the  Laplacian  hypothesis  the 
planets  have  contracted  from  the  dimensions  of  their  satellite  orbits, 
every  planet  must  rotate  in  a  shorter  period  than  that  of  the  revolu- 
tion of  its  innermost  satellite.  This  certain  consequence  of  the  theory 
is  violated  in  the  case  of  the  inner  satellite  of  Mars,  which  makes 
its  revolution  in  about  eight  hours  while  Mars  turns  on  its  axis  in  a 
period  of  some  24  hours.  There  is  also  an  important  discrepancy 
between  theory  and  observations  in  the  case  of  the  inner  ring  of 
Saturn,  the  particles  of  which  make  a  revolution  in  about  five  hours 
while  the  planet  rotates  on  its  axis  in  a  period  of  a  little  more  than 
10  hours. 

According  to  the  Laplacian  theory,  the  more  remote  planets  are 
older  than  the  interior  ones.  The  excess  of  their  ages  is  not  known, 
but  certainly  it  must  be  very  great  according  to  the  theory.  Perhaps 
Saturn  is  a  thousand  times  as  old  as  the  earth.  When  we  consider 
how  much  greater  its  orbit  is  than  that  of  the  earth,  and  how  long 
it  must  have  taken  the  sun  to  contract  from  the  dimensions  of  the 
earth  to  its  present  size,  this  does  not  seem  an  unreasonable  estimate. 
It  follows  that  if  Saturn  were  originally  in  a  state  similar  to  that 
of  the  original  earth  it  should  be  much  farther  advanced  in  its  evo- 
lution. It  was  seen  in  the  discussion  of  planets  that  Saturn  is  yet 
in  a  very  primitive  state.  Of  course,  being  larger,  it  would  undergo 
its  evolution  more  slowly,  but  it  seems  to  strain  the  probabilities  of 
the  matter  to  suppose  that  its  difference  in  size  could  offset  its 
supposed  great  difference  in  age.  It  is  thus  seen  that  the  Laplacian 
theory  is  in  many  places  in  direct  conflict  with  the  observations. 
These  discrepancies,  however,  have  nearly  all  been  discovered  since 
the  theory  was  originally  formulated. 

About  ten  years  ago  Professor  Chamberlin  and  the  writer 
undertook  to  make  a  critical  examination  of  the  Laplacian  theory, 
both  for  internal  discords  and  harmonies,  and  to  find  disagreements 
and  agreements  with  the  facts  given  by  observation.  This  study 
revealed  inconsistencies  in  the  theory  itself,  as  well  as  contradictions 
to  the  observed  phenomena,  some  of  which  have  been  noted  above, 
which  compel  its  radical  modification.  It  is  certain  now  that  the 
ring  hypothesis  as  to  the  origin  of  the  planets  can  no  longer  be  held 
as  a  possibility.  This  does  not  mean  that  the  Laplacian  theory  has 


244  ASTRONOMY 

not  been  of  the  greatest  importance  in  the  development  of  science, 
but  it  simply  indicates  that  greater  knowledge  has  shown  us  its 
imperfections,  and  how  we  may  use  it  as  a  stepping-stone  to  a  more 
perfect  picture  of  the  origin  and  evolution  of  the  solar  system. 

Planetesimal  Theory.  The  solar  system  exists  and  is  in  the 
midst  of  an  evolution;  the  problem  is  to  trace  out  the  mode  of  this 
evolution.  The  Laplacian  theory  has  been  seen  to  have  fatal  weak- 
nesses and  to  be  no  longer  tenable.  We  shall  now  outline  a  theory 
which  has  been  developed  by  Professor  Chamberlin  and  the  author 
to  take  its  place. 

Instead  of  supposing  that  the  solar  system  started  from  a  vast 
gaseous  mass  in  equilibrium  under  the  law  of  gravitation  and  the 
laws  of  gaseous  expansion,  the  Planetesimal  Hypothesis  postulates 
that  the  matter  of  which  the  sun  and  planets  are  composed  was  at 
a  previous  stage  of  its  evolution  in  the  form  of  a  great  spiral  swarm 
of  separate  particles  whose  positions  and  motions  were  dependent 
upon  their  mutual  gravitation  and  their  velocities.  Gaseous  expan- 
sion preserved  the  dimensions  of  the  Laplacian  nebula  but  had  no 
sensible  influence  in  the  spiral.  Because  of  the  fact  that  every 
particle  according  to  this  theory  is  considered  as  being  an  essentially 
independent  unit  it  is  called  the  planetesimal  theory.  Before  consid- 
ering in  detail  the  planetesimal  hypothesis,  and  before  proceeding  to 
a  discussion  of  its  merits,  attention  should  be  called  to  the  fact  that 
there  is  not  in  all  the  heavens  a  single  example  known  of  a  nebula 
of  the  Laplacian  type.  On  the  other  hand,  recent  discoveries,  par- 
ticularly those  made  at  the  Lick  Observatory,  show  that  the  spiral 
nebula  is  not  only  a  common  form  but  is,  indeed,  the  dominant 
type.  There  are  within  range  of  our  instruments  at  least  ten  times 
as  many  of  them  as  of  all  other  types  combined,  and  they  range  in 
extent  and  brightness  from  the  great  Andromeda  nebula  down  to 
small  faint  masses  which  are  barely  distinguishable  with  long  expo- 
sure photographs  taken  with  the  most  powerful  instruments. 

Before  considering  the  evolution  of  our  system  from  a  spiral 
nebula,  a  suggestion  as  to  its  origin  will  be  developed.  It  is,  of  course, 
understood  that  the  theory  is  independent  of  the  correctness  of  this 
suggestion.  It  has  the  merit  of  giving  us  a  full  picture  of  the  course 
of  evolution  and  of  showing  the  dynamical  condition  of  a  nebula. 
It  has  been  seen  above  that  there  are  within  the  range  of  our  present 


ASTRONOMY 


245 


instruments  at  least  a  hundred  millions  of  suns,  and  it  is  found,  from 
the  observations  of  their  apparent  motions  and  their  actual  motions 
in  the  line  of  sight  by  means  of  the  spectroscope,  that  on  the  average 
they  are  moving  with  high  speed.  Though  there  are  undoubtedly 
parallelisms  and  some  degree  of  orderliness  in  their  motions,  never- 
theless, it  is  almost  certain  that  now  and  then  two  suns  will  pass 
near  each  other.  A  computation,  based  on  suppositions  which  seem 
to  be  reasonable  as  to  the  dimensions  of  the  sidereal  system  and  the 
number  of  stars  in  it,  shows  that  in  the  long  run  a  given  sun  will 


Fig.  108.    The  Origin  of  Elliptical  Orbits  of  Matter  Ejected 
from  the  Sun  at  the  Time  a  Star  is  Passing 

pass  near  enough  to  another  sun  to  cause  serious  disturbances  about 
once  in  a  billion  years. 

Now  consider  a  star  passing  near  our  sun,  and  remember  that 
the  latter  is  a  highly  heated  body  subject  to  explosive  forces  which 
even  at  frequent  intervals  hurl  matter  up  from  its  surface  to  heights 
of  several  hundred  thousand  miles.  In  Fig.  108  let  S  represent  our 
sun,  and  0  the  orbit  of  a  star  passing  by  it.  Consider  the  visiting 
star  when  it  is  at  the  position  S^  It  raises  enormous  tides  on  our 
sun,  their  height  depending  upon  its  distance  and  mass.  One  tide 
is  on  the  side  toward  Si,  and  the  other  tide  on  the  opposite  side. 
Instead  of  being  a  few  feet  high,  it  is  reasonable  to  suppose  that 
they  are  many  thousands  of  miles  high.  The  ejections  from  our  sun 


246  ASTRONOMY 

under  those  circumstances  are  most  violent  and  to  the  greatest 
distances  in  the  directions  toward  and  away  from  S^  For  simplicity, 
let  us  consider  only  the  matter  ejected  toward  S^  If  S1  were 
standing  still  this  matter  would  proceed  toward  it  a  certain  distance, 
depending  upon  the  speed  with  which  it  left  the  sun,  and  then  would 
either  fall  back  upon  the  sun  or  go  to  S1}  depending  upon  which 
had  the  dominating  attraction  for  it.  But  instead  of  standing  still 
Si  is  moving  forward  rapidly  in  its  orbit.  Suppose  the  direction  of 
motion  is  that  indicated  by  the  arrow  in  Fig.  108.  After  a  certain 
interval  Si  has  moved  forward  to  the  point  S2.  At  this  place  it  is 
attracting  the  ejected  mass  P  nearly  at  right  angles  to  its  original 
line  of  projection.  Consequently,  it  causes  its  orbit  to  curve  in  the 
direction  in  which  Si  is  going.  The  visiting  star  will  go  on  in  its 


Fig.  109.     The  Origin  of  a  Spiral  Nebula 

orbit  and  leave  P  behind  revolving  around  the  sun  in  the  dotted 
ellipse  C.  In  a  similar  manner  the  mass  P  will  be  bent  from  the 
straight  line  of  its  ejection  in  the  direction  indicated  in  the  diagram, 
and  will  be  left  revolving  in  the  ellipse  C".  Therefore,  as  the  visiting 
star  passes  near  the  sun  it  stimulates  the  ejection  of  material  and 
causes  it  to  deviate  from  the  original  line  of  its  motion  so  that  instead 
of  falling  back  on  the  sun  it  is  left  revolving  about  it  in  elliptical 
orbits. 

This  process  of  ejection  obviously  would  not  take  place  at  only 
one  instant,  while  Si  was  passing  our  sun.  We  now  consider  the 
result  of  its  taking  place  continually  during  the  passage.  Many 
particles  are  ejected  and  they  move  along  the  dotted  lines  of  Fig. 
109.  At  a  given  time  they  are  on  the  full  lines  of  Fig.  109,  which 
are  seen  to  constitute  the  arms  of  a  spiral  with  two  approximately 
symmetrical  parts.  If  this  theory  is  correct,  we  should  find  that  the 
spiral  nebulas  have  two  arms  reaching  out  from  a  central  sun  in 


ASTRONOMY  247 

opposite  directions  which  are  curved  in  the  same  direction.  The 
particles  on  the  spiral  are  not  moving  along  its  arms,  but  approxi- 
mately at  right  angles  to  them.  The  particles  near  the  center  move 
faster  than  those  far  away,  and  consequently  the  older  the  spiral 
nebula  and  the  larger  its  central  mass  relatively  to  the  total  mass 
of  the  scattered  material,  the  closer  is  its  coil. 


Fig.  110.     Spiral  Nebula  in  Canes  Venatici.     Photographed  at  the 
Yerkes  Observatory 

The  question  now  arising  is  whether  the  spiral  nebulas  which 
are  known  have  the  characteristics  which  would  be  predicted 
according  to  this  theory.  Fig.  110  is  a  photograph  of  one  of  these 
objects.  It  is  seen  that  it  is  composed  of  two  arms,  in  a  general 
way  symmetrical,  which  reach  out  from  the  opposite  sides  of  a  central 
nucleus,  or  sun.  It  is  found  that  they  always  have  two  arms  which 


248  ASTRONOMY 

can  be  more  or  less  definitely  made  out,  radiating  from  the  center 
in  this  fashion.  The  suggestion  of  their  origin  seems  to  be  in 
harmony  with  their  appearance,  though  it  can  not  be  regarded  as 
demonstrated  that  this  is  the  true  explanation  of  their  mode  of 
development.  Fig.  Ill  shows  one  of  these  objects  which  is  edgewise 


Fig.  111.     Spiral  Nebula  in  Adromed  Seen  Edgewise.     The  Dark  Peripheral  Material 
Causes  a  Dark  Streak  by  Eclipse.      Photographed  at  the  Lick  Observatory 

to  us.    The  dark  streak  down  it  is  due  to  opaque,  cooler  absorbing 
material  on  its  periphery. 

According  to  the  planetesimal  theory  the  planets  grew  up  around 
the  nuclei  on  the  arms  of  the  spirals  from  which  our  system  devel- 
oped, whatever  may  have  been  its  origin.  It  is  clear  that  if  the 
origin  of  the  spiral  were  as  outlined  above,  we  should  not  expect  to 
find  the  arms  perfectly  uniform  because  the  ejection  from  our  sun 
would  not  take  place  uniformly.  The  photographs  show  many 


ASTRONOMY  249 

irregularities  and  local  condensations  on  the  arms.  These  nuclei 
circulating  around  the  central  sun  and  crossing  the  orbits  of  many 
other  particles  also  circulating  around  the  center,  gradually  sweep 
them  up  and  in  the  course  of  time  absorb  all  oi  Qie  small  masses 
in  the  system  whose  orbits  they  cross.  In  this  manner  there  eventu- 
ally evolves  a  system  consisting  of  a  central  sun  and  a  number  of 
large  masses  spaced  out  so  that  they  never  approach  very  near  one 
another,  and  no  small  ones  except  possibly  in  zones  which  were  not 
occupied  by  any  dominant  nucleus. 

Let  us  see  whether  this  theory  is  in  harmony  with  the  chief 
facts  presented  by  the  solar  system.  According  to  it  all  the  planets 
should  revolve  in  the  same  direction,  and  such  is  found  to  be  the 
case.  According  to  it  their  planes  should  be  approximately  the 
same,  though  not  necessarily  the  same,  for  the  initial  ejections  would 
not  necessarily  be  exactly  toward  or  from  the  passing  sun.  Here, 
again,  the  theory  and  observations  are  in  harmony.  According  to 
this  theory  the  planets  are  all  the  same  age,  and  the  differences  in 
the  state  of  their  development  are  only  because  of  their  different 
dimensions  and  different  constitutions.  The  facts  given  by  obser- 
vation are  in  this  respect  much  more  in  harmony  with  this  theory 
than  with  the  Laplacian.  One  of  the  difficulties,  at  least  at  first 
thought,  arises  from  the  fact  that  when  the  visiting  sun  had  passed 
on,  the  orbits  of  the  individual  nuclei  and  particles  should  be  on 
the  average  considerably  more  eccentric  than  the  orbits  of  the 
planets.  But  a  mathematical  examination  of  the  question  shows  that 
the  orbits  of  the  planets  become  more  nearly  circular  on  account  of 
their  collisions  with  the  scattered  material  which  the  planets  sweep 
up  in  their  motions  around  the  sun.  Consequently,  the  more  a 
planet  grows  by  the  accretion  of  this  scattered  material  the  more 
nearly  circular  its  orbit  becomes.  It  is  significant  that  in  our 
system  the  great  planets  all  have  very  nearly  circular  orbits,  while 
the  smaller  ones  have  more  elongated  orbits,  and  the  orbits  of  the 
planetoids  are  in  many  cases  very  much  elongated.  There  is  here 
perfect  harmony  between  the  theory  and  the  facts  given  by  observa- 
tions. Similar  results  follow  when  we  consider  the  inclinations  of  the 
orbits  to  one  another.  The  more  matter  a  planetary  nucleus  acquires 
by  collision  with  the  scattered  material,  the  more  nearly  will  its 
orbit  fall  into  the  average  plane  of  the  system.  It  is  found  that 


250  ASTRONOMY 

the  great  planets  move  in  orbits  which  are  almost  in  the  same  plane, 
while  the  smaller  ones  deviate  some,  and  in  many  cases  the  planetoids 
very  much.  Thus,  again,  there  is  harmony  between  theory  and 
observations. 

In  discussing  the  Laplacian  theory,  it  was  found  that  difficulties 
arise  because  of  the  retrograde  revolution  of  certain  satellites. 
The  question  arises  whether  the  planetesimal  theory  has  difficulties 
in  this  same  respect.  According  to  the  planetesimal  theory  the 
satellites  have  evolved  from  small  secondary  nuclei  which  were  revolv- 
ing around  the  central  sun  in  close  proximity  to  the  larger  nuclei 
which  developed  into  planets.  There  is  no  reason  why  these  sec- 
ondary nuclei  should  not  originally  have  revolved  around  the  planets 
in  any  direction.  A  discussion  of  the  matter  shows  that  those  which 
revolve  in  any  direction  except  in  that  in  which  the  planet  revolves 
have  a  tendency,  because  of  collisions  with  the  scattered  material, 
to  fall  upon  the  planet  and  to  become  a  part  of  it.  This  is  particu- 
larly true  unless  they  are  far  from  it.  Consequently,  we  should 
expect  to  find  the  satellites  on  the  whole  revolving  in  the  forward 
direction,  though  not  necessarily  all  in  that  direction.  And  further- 
more, there  is  no  reason  according  to  this  theory  why  a  satellite 
should  not  revolve  around  the  planet  in  a  shorter  period  than  that 
of  the  rotation  of  the  planet  itself. 

According  to  the  Laplacian  theory  it  is  difficult  to  account 
for  the  forward  rotations  of  the  planets.  The  forward  rotation  of 
the  planets  is  to  be  expected  under  the  planetesimal  theory,  because 
it  can  be  shown  that  the  collisions  of  the  scattered  material  with 
the  planetary  nuclei  have,  on  the  average,  a  tendency  to  make  them 
rotate  in  the  direction  of  their  revolution.  This  tendency  is,  besides, 
the  greatest  in  their  equatorial  zones,  and  if  they  are  in  a  fluid  state 
should  give  to  their  equators  a  greater  speed  of  rotation  than  to  the 
higher  latitudes.  All  of  these  consequences  of  the  theory  are  in  per- 
fect harmony  with  the  facts. 

Conclusion.  We  shall  sum  up  in  a  few  words  the  general  picture 
of  the  origin  and  development  of  astronomical  bodies,  remembering, 
however,  that  the  problem  is  a  vast  one  and  that  the  chances  for 
actual  errors  and  imperfections  in  our  theories  are  very  great.  We 
regard  matter  as  being  in  its  most  primitive  state  when  it  is  spread 
out  in  widely-scattered,  irregular  nebulas.  (See  Fig.  104.)  These 


ASTRONOMY  251 

objects  are  supposed  to  develop  continually;  that  is,  they  are  sup- 
posed not  only  to  have  originated  in  the  past,  but  are  even  now 
being  evolved,  and  will  continue  to  evolve  in  the  future.  These 
nebulous  masses,  under  the  chemical  and  gravitational  forces,  became 
organized  into  suns  and  systems  of  suns.  The  suns  now  and  then 
passing  near  one  another  develop  spiral  nebulas.  The  nuclei  on  the 
arms  of  the  spirals,  sweeping  up  this  finely  scattered  material,  grow 
into  planets,  or  at  any  rate  into  bodies  secondary  in  dimensions  com- 
pared with  the  central  sun.  The  length  of  time  required  for  this 
evolution  is  altogether  beyond  calculation  at  the  present  time. 
Considering  the  earth,  we  think  of  it  as  having  grown  up  rapidly 
at  first,  and  more  slowly  later,  by  the  accretion  of  the  scattered 
material.  Originally  it  was  perhaps  too  small  to  hold  an  atmosphere, 
which  was  subsequently  acquired  by  the  expulsion  of  gases  from  the 
material  of  which  it  was  composed,  as  it  ground  together  under 
pressure  and  became  heated  by  its  contraction.  After  acquiring 
an  atmosphere  and  water  it  became  habitable,  at  least  for  low  forms 
of  life.  At  the  present  time  it  is  not  growing  at  a  sensible  rate,  and 
so  far  as  can  be  seen  will  remain  approximately  in  its  present  state 
for  an  extremely  long  time.  It  seems  to  be  threatened  only  by  a 
possible  failure  of  the  sun's  light  and  heat.  Until  we  know  more 
exactly  than  at  the  present  time  the  sources  of  the  sun's  heat,  we 
can  not  estimate  how  soon  the  changes  in  the  amount  of  light  and 
heat  received  from  the  sun  will  have  sensible  influences  upon  the 
earth.  One  event  in  the  remote  future  seems  probable,  if  not  certain. 
It  is  that  once  again  our  sun  will  pass  near  some  other  sun,  when 
the  present  planetary  system  will  be  destroyed,  perhaps  to  give 
place  to  a  new  one  running  through  a  somewhat  similar  cycle. 


INDEX 


A  Page 

Astronomical  problems  respecting  earth 7 

Astronomy 1-251 

comets  and  meteors 185 

constellations 61 

cosmogony,  or  the  evolution  of  worlds. . 235 

earth  as  an  astronomical  body 7 

moon 110 

preliminary  considerations 1 

sidereal  system 216 

solar  system 137 

sun 197 

time 100 

Atmosphere 

effects  of,  on  climate 25 

escape  of 23 

of  moon 120 

refraction  of  light  by 28 

B 

Bootes...  95 


C 

Calendar 109 

Canis  Major 100 

Cassiopeia 92 

Civil  and  astronomical  days.  '. 107 

Comets 

capture  of 187 

celebrated 190 

dimensions  and  masses  of 186 

orbits  of 185 

Comets  and  meteors,  relation  of 194 

Constellations 61 

application  of  declination  to  location  of  stars 71 

Bootes , 95 

Canis  Major 100 

Cassiopeia 92 

determination  of  right  ascension  of  meridian  at  any  time 69 

Gemini..  100 


254  INDEX 

Page 
Constellations 

Leo 96 

magnitudes  of  stars 82 

Milky  Way 88 

naming  the  stars 79 

number  of  stars 85 

origin  of 72 

Orion '. 97 

pole  star 90 

problem  of  locating. , 61 

proper  motions  of  stars 87 

Scorpio 95 

star  catalogues 80 

systems  of  coordinates  for  locating 

comparison  of 68 

ecliptic 67 

equator 64 

geographical 62 

horizon '. 63 

Taurus 96 

Cosmogony 235 

evolution 235 

historical 237 

planetesimal  theory 244 

test  of  Laplacian  theory , 241 

D 
Distance 

of  moon 113 

of  planets 141 

of  sun 141 

of  stars 218 

E 

Earth  as  an  astronomical  body 7 

astronomical  problems  respecting 7 

condition  of  interior  of 15 

density  of 14 

oblateness  of 10 

orbit  of 48 

proofs  of  its  sphericity 

revolution  of ,44 

rotation  of 30 

size  of 13 

Earth's  atmosphere 

climatic  effects  of 25 

composition  of 

height  of 18 

Earth's  orbit,  shape  of 48 


INDEX  255 

Page 
Eclipses 

of  moon 131 

of  sun 132 

Ecliptic,  obliquity  of 49 

Ecliptic  systems  of  coordinates 67 

Equator  system  of  coordinates 64 

Equinoxes,  precession  of 50 

Evolution 235 

F 

First-magnitude  stars ; 85 

G 

Gases,  kinetic  theory  of 21 

Gemini 100 

Geographical  system  of  coordinates 62 

H 

Horizon  system  of  coordinates 63 

J 

Jupiter 170 

L 

Laplacian  theory,  test  of 241 

Latitude 

different  kinds  of 13 

variation  of .' 40 

Laws 

of  gravitation 139 

of  motion 32 

Leo 96 

Light  and  heat  received  from  sun 197 

Lyra 93 

M 

Magnitudes  of  stars 82 

Mars 161 

Mass  of  moon 119 

Mean  solar  time 103 

Mercury  and  Venus 159 

Meteorites. 196 

Meteors  or  shooting  stars 192 

influences  of,  on  the  earth 195 

meteorites 196 

relation  of  comets  and  meteors. .  194 


256  INDEX 

Page 

Milky  Way  or  galaxy 88 

Moon 110 

actual  motion  of , 117 

apparent  motion  among  stars 110 

atmosphere  of 120 

distance  of 113 

distribution  of  sunlight  and  moonlight 113 

eclipses  of 131 

eclipses  of  sun 132 

light  and  heat  received  by  earth  from 121 

mass  of 119 

phases  of Ill 

relative  number  of  eclipses  of  sun  and  moon  as  observed  from  any 

one  place 133 

size  of 118 

surface  conditions  on 123 

temperature  of 122 

Motion,  laws  of 32 

N 

Neptune 181 

O 

Orbits  of  planets 138 

Origin  of  constellations 72 

Orion 97 

P 

Place  of  change  of  date 107 

Planetesimal  theory 244 

Planetoids 152 

Planets 

dimensions  and  masses  of 144 

distances  of 141 

periods  of 147 

two  groups  of 151 

Pole  star,  how  to  find 90 

R 

Revolution  of  earth 
proved  by 

aberration  of  light 46 

laws  of  motion 42 

parallax  of  stars 44 

spectroscope 47 

Right  ascension  of  meridian 69 


INDEX  257 


Rotation  of  earth 30 

analogy  with  other  heavenly  bodies 37 

laws  of  motion 32 

proved  by  eastward  deviation  of  falling  bodies 34 

proved  by  Foucault's  pendulum  experiment 36 

proved  by  its  shape 35 

uniformity  of 38 

S 

Saturn 175 

Science 

contributions  of  astronomy  to 3 

origin  of 2 

value  of 1 

Scorpio 95 

Seasons 

causes  of 51 

effect  of  eccentricity  of  earth's  orbit  upon 58 

lag  of 57 

Sidereal  system 216 

distribution  of  stars 216 

double  stars 224 

groups  of  stars 219 

nebulas 233 

spectroscopic  binary  stars : 227 

temporary  stars 231 

variable  stars 229 

Sidereal  month Ill 

Sidereal  time 101 

Sidereal  year 108 

Size  of  moon 118 

Solar  system .  137 

dimensions  and  masses  of  planets 144 

distances  of  planets 141 

historical 237 

Jupiter 170 

law  of  gravitation ». 139 

Mars 161 

members  of 137 

Mercury  and  Venus 159 

Neptune 181 

orbits  of  planets 138 

periods  of  planets 147 

planetoids 152 

Saturn 175 

two  groups  of  planets 151 

Uranus 179 

zodiacal  light  and  gegenschein 157 

Solar  time..  102 


258  INDEX 

Page 

Spectrum  analysis 210 

Star  catalogues 80 

Stars 

distribution  of 216 

double 224 

first-magnitude 85 

groups  of 219 

location  of 71 

magnitudes  of 82 

Milky  Way '. 88 

naming  of 79 

nebulas 233 

number  of 85 

Pole  star 90 

proper  motions  of 87 

spectroscopic  binary 227 

temporary 231 

variable. . 229 

Sun 197 

different  layers  of 206 

light  and  heat  received  from 197 

motion  of,  with  respect  to  stars * 42 

source  of  heat  of 200 

spectrum  analysis 210 

spots 204 

Sunlight  and  moonlight,  distribution  of 113 

Surface  conditions  on  moon. .  123 


T 
Table 

binary  stars  whose  masses  and  distances  are  known 226 

comparative  gravity  of  sun  and  planets 147 

data  from  which  to  compute  times  favorable  for  observation  of  planets  150 

densities  of  sun  and  planets 146 

list  of  constellations  with  right  ascensions  and  declinations 73 

list  of  first-magnitude  stars 84 

number  of  stars  visible  to  naked  eye 85 

planets  in  order  from  sun  with  apparent  and  actual  diameters 144 

surface  and  volume  of  planets  as  compared  to  earth 145 

Taurus 96 

Temperature  of  moon 122 

Time , 100 

calendar 109 

civil  and  astronomical  days 107 

definition  of  equal  intervals  of 100 

mean  solar 103 

place  of  change  of  date 107 

sidereal 101 

sidereal  year 108 


INDEX  259 

Page 
Time 

solar 102 

standard 105 

Tropical  year 108 

U 

Uranus , .  179 

Z 

Zodiacal  light  and  gegenschein 157 


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NOV  12  1957 


21-100m-l,'54(1887sl6)476 


4   1929 
M 


Mr 

THE  UNIVERSITY  OF  CALIFORNIA  UBRARY 


